Calculus: Integral with adjustable bounds. For example, a rectangle has a length of 5 units and a width of 2 units. Method 2 Finding a Similar Figure Using the Scale Factor 1 Find the side lengths of the figure. a) If the image has to be enlarged. This means that the image, A', is twice as large as the pre-image A. Assistant Professor of Mathematics. Follow the steps below: Firstly, you have to select the number of input values. First of all, select which quantity you want to do calculations for, From the next drop down list, select whether you want to calculate real size, scale size, or scale factor, After you make a selection, go for entering the wanted parameters in their designated fields and select the respective units, Scaled size of the area, volume, or length. Quantum physicist's take on boiling the perfect egg. In the same way, if you have to draw a smaller triangle similar to the giant triangle, you need to divide the length of the sides of the original triangle by using the scale factor formula. A scale drawing is an accurate plan of the real object, drawn using a scale factor to make the drawing small enough to handle. The centre of dilation can be calculated by using the following formula: x o = ( k x 1 x 2 k 1), y o = ( k y 1 y 2 k 1) Where k is the scale factor of dilation and (x o ,y o) is the centre of the. How to Calculate priceeight Density (Step by Step): Factors that Determine priceeight Classification: Are mentioned priceeight Classes verified by the officials? So instead of this side being 2 = 6 Dimensions of the original shape, Dimensions of the original shape = 6 2 = 3 units, b.) First of all, converting measurements from inches to centimeters as follows: . Includes times for quarter and half-boiled eggs. practice, you might be able to do it without drawing pictures but they're saying some You can find the scale factor of an irregular shape just as you would find the scale factor of a regular shape. This means that 868 Specialists. wikiHow is where trusted research and expert knowledge come together. Let's draw a rectangle This means the image is scaled down. Increase the dimensions of the given figure using scale factor \(5\). Make an outsized effort! What would be the real length of the object with a scale length of 64 cm into inches and a scale factor of 5 1 in inches? Dilation with scale factor 2, then multiply by 2. Lets find how! is indeed five square units. Example 2. Each point is stretched outwards from the center point D by multiplying distances by the scale factor. So every other linear measure is multiplied by 5 to scale them up. If the scale factor is a whole number, the copy will be larger. By taking the time to explain the problem and break it down into smaller pieces, anyone can learn to solve math problems. The problem should tell you that the shapes are similar, or it might show you that the angles are the same, and otherwise indicate that the side lengths are proportional, to scale, or that they correspond to each other. The definition of scale factor is that it is a number that multiplies times a given quantity to produce a smaller or larger version of the original number. In case of any queries, you can reach back to us in the comments section, and we will try to solve them. How does it sound? Scale Factor isutilised to scale the shapes in various dimensions. is if you scale something, if you scale the sides of Basically, the scale factor is used to increase or decrease the size of any geometrical figure. Go ahead and convert your own value of. I am working with a triangle, and he does not include that in this video. Q.5. Well our area, and this Polygon Q, and so our area is going This is known as the scale factor. A triangle is a polygon that has three vertices. A figures size is enlarged or reduced than the dimensions of the original shape, and the scale factor is known. What about going through the scale factors of some important models as described below on the table: What about resolving a couple of examples to understand together what measurements the scale factor deals with. Internxt's free Byte Converter: Find out how much storage you have, how many gigabytes are in a terabyte, and convert to-and-from B, KB, MB, GB, and TB. For example, if the side length of a square is 6 units and if the size of the square has been increased such that the side length of the square becomes 18 units, let us find the scale factor. How do you find the linear scale factor of an irregular shape? by a factor of nine. One object can have different scales too. Here, the scale factor can be calculated using the basic formula given in the previous section. A scale factor ratio can be expressed as a fraction, 12\frac{1}{2}21, or a colon, 1:2. Direct link to David Severin's post You may not be able to "p, Posted 2 years ago. This shows that a scale factor of 0.5 changed the figure to a smaller one. to be four times eight which is 32. Its used to draw any given figures enlarged or reduced shape, as well as to discover the missing length, area, or volume of an enlarged or reduced figure. When a scale factor is applied, the size of the object is increased or decreased according to the desired scale. The scale factor formula = Smaller figure dimensions Larger figure dimensions. Physics Calculators Scale Factor Calculator, For further assistance, please Contact Us. Use this triangle scale factor calculator to find the scale factor between two similar triangles. The scale factor of 3 means that it is 3 times as long in all dimensions. Output: 48/12 = 4 which is the scale factor times the scale factor. Scale is a ratio that is used to define the relation of the actual figure or object with its model. When shrinking the shape, the smaller measurement is the numerator, and the larger measurement is the denominator. Using a Calculator for the SAT Math Level 2 . Ans: We have the given dimensions of the giant rectangle are \({\rm{40\,cm}}\) and the dimensions of the smaller rectangle are \({\rm{20\,cm}}\).In this diagram, the shape is scaled down.\({\rm{The\;scale\;factor\;formula}} = {\rm{Greater\;shape\;dimensions}} \div {\rm{Smaller\;shape\;dimensions\;}}\)So, \(\frac{{20}}{{40}} = \frac{1}{2}\)Hence, the scale factor used to create the smaller rectangle is \(\frac{1}{2}\). "Polygon Y has an area of 11 square units. The basic formula to find the scale factor of a figure is: Get Assignment. wide and we need to reduce it by25%, or one-quarter (14\frac{1}{4}41). is a scaled copy of Polygon P. So let's start with Polygon P. And I will do this in red. Scaling up, the ratio is. This means that, To find the scale factor of two similar triangles one needs the measures of at least one pair of corresponding sides. This article has been viewed 816,652 times. We will place the given values in the formula: Scale factor = Dimension of the new shape Dimension of the original shape. Direct link to Charlie Hu's post The scale factor of 3 mea, Posted 3 years ago. Good enough! scaled it by one half, and now what is our area going to be? 20+ tutors near you & online ready to help. The scale factor is used to solve geometric problems. These problems involve multiplication or require you to simplify fractions. Thus, you can calculate a scale factor using any dimension you are given. If the scale factor is less than 1 (0< k <1), the image is contracted. Solution: The given dimension of the bigger polygon is 40 units. A scale factor of 0.5 means that the changed image will be scaled down. Now that you know how to find the scale factor of two triangles, you can look at these other exciting tools: To find the scale factor of two triangles, follow these steps: If an isosceles triangle RST was dilated by a scale factor of 1/2, and the legs of the dilated triangle (R'S' and R'T') measured 8 units, the length of the legs of the original triangle must be 16 units. The given dimension of the smaller polygon is 20 units. What is a scale factor of \(2\)?Ans: The scale factor \(2\) means the new shape obtained after scaling up the original figure by \(2\) or making the dimensions of the original figures shape double.Below is an example for a better understanding of the scale factor of \(2\). Q.4. Dilating triangle ABC by a scale factor of -2 results in triangle DEF with vertices D (-2, -6), E (-4, -6), and F (-4, -2). To go from legs of12cmto legs of36cm, we needed to multiply12cmtimes3. Hence, you can see that the scale factor is greater than the number \(1\). a) If the image has to be enlarged, the scale factor is more than 1 (k > 1). It should be noted that the scale factor helps in changing the size of the figure and not its shape. It is used to compare two similar geometric shapes and also in other fields like cooking, where the ingredients can be reduced or increased according to the given situation. Triangle Scale Factor Calculator Another way to describe a scale factor is that it's a multiplier. Scaling down means that a larger figure is reduced to a smaller one. Scale Factor of a Triangle Similar triangles have identical shapes, and the three angles are also identical. This formula can also be used to calculate the dimensions of the new figure or the original figure by simply substituting the values in the formula. Polygon Q's area is what The scale factor forscaling upis aratio greater than1. Substituting the values in the formula for all the three dimensions: a.) Therefore, the original dimensions of a triangle were = 3 units, 5 units, and 6 units. If you want to learn how to find the scale factor in chemistry, keep reading the article! 3x4x3x3 = 108 units squared. Free Quadrilaterals calculator - Calculate area, perimeter, diagonals, sides and angles for quadrilaterals step-by-step . Scale factor calculator triangle - This type of dilation occurs for a function y = f(x) which dilates the function by a scale factor C using the following equation: $$ Y = . For example, if a circle needs to be increased in size using a scale factor of 4, and the circumference of the circle is 7 units. And now that they gave everyone the "plus" feature for free until 20th April, best app I've ever used, This app has helpede in so many tests, not getting a perfect score but more than enough to get satisfied, 100% recommended. Since 12 is smaller than 36, it means the original figure has been reduced in size. Next, measure (or read) any side of the figure and do some math. Dont shrink from it! Direct link to william.franco's post I am working with a trian, Posted 4 years ago. The original shape has been reduced if the scale factor is less than the number \(1\). Ascale factorin math is the ratio between corresponding measurements of an object and a representation of that object. Scale factor is how we ensure the representation of the object differs only in size from the original object. So the new area could be found 3 x 4 x scale factor x scale factor. For example, a scale of 1:3 means 1 on the map represents the size of 3 in the real world. the idea that area will grow, the factor with which area grows is the square of the scale factor. length three instead of nine. Great learning in high school using simple cues. Math can be tough to wrap your head around, but with a little practice, it can be a breeze! You may be astounded enough, but it really works. One way to determine mathematic tasks is to consider the various operations that can be performed on numbers. So we're gonna scale it by one half. This is the scale factor we multiply a side length of triangle ABC by to find its corresponding side length in DEF. Enjoy! https://www.cuemath.com/geometry/scale-factor/, http://www.mathsisfun.com/geometry/similar.html, http://www.virtualnerd.com/pre-algebra/ratios-proportions/similar-figures-indirect-measurement/similar-figures/find-scale-factor-similar-figures, http://www.virtualnerd.com/pre-algebra/ratios-proportions/missing-measurements-similar-figures-scale-factor.php, http://www.vias.org/physics/bk1_03_02b.html, trouver un coefficient de proportionnalit. 2 = 10 Dimensions of the original shape, Dimensions of the original shape = 10 2 = 5 units, c.) 2 = 12 Dimensions of the original shape, Dimensions of the original shape = 12 2 = 6 units The basic formula that is used for calculating the scale factor is, Scale factor = Dimension of the new shape Dimension of the original shape. Scale Factor = * (Scale Volume/Real Volume) Scale Volume = (d1/d2) * Real Volume Real Volume = (d1/d2) * Scaled Volume All of the above expressions are also taken into consideration by the scale factor calculator while doing instant calculations. Identify the original points of the polygon. Enter the real and scaled value of the physical parameter (volume, length, or area) and the calculator will calculate the actual scale factor for it. However, with a little bit of practice, anyone can learn to solve them. here, it's a quadrilateral, it's in fact a rectangle and its area is just going When enlarging the shape, the larger measurement is the numerator, and the smaller measurement is the denominator. As a small thank you, wed like to offer you a $30 gift card (valid at GoNift.com). If we're going from an Celia drew a scaled version of Polygon Y using a scale factor of 3 and labeled it Polygon Z" is my question. two, three, four, five, it's five high, and it you multiply by three. You can use the scale factor to find the missing side lengths of a figure. By using our site, you agree to our. To get the second, smaller figure, we multiply 211721\times \frac{1}{7}2171; the figure on the right uses a scale factor of1:7,17\frac{1}{7}71, oroneseventh. It is a number by which the size of any geometrical figure or shape can be changed with respect to its original size. A scale factor gives the ratio of the representation to the actual object. Deal with math equations. Yes, although the fraction could be either less than or greater than 1. The new dimensions of the triangle are: 6 units; 10 units; and 12 units; The scale factor = 2 Scale factor = Dimensions of the new shape Dimensions of the original shape. So one way to think I can help you with any mathematic task you need help with. So Polygon P, let's just say, I'm just gonna create For example if you are scaling down from a triangle with a 15 cm base to one with a 10 cm base, you would use the ratio. over here being eight, the corresponding side For example, the original figure of a square has one of its sides as 6 units. You can find the scale factor of corresponding angles, sides, and even diagonals. Pause this video and see Math can be a difficult subject for many people, but it doesn't have to be! The same concept applies to any two-dimensional shape. Good and works on just about every problem plus tells you how to slove a problem step by step no ads either. Dismiss Home News Feed Resources Profile People Classroom App Downloads About GeoGebra Contact us : office@geogebra.org Terms of Service - Privacy - License Language: English 2023 GeoGebra Can somebody please help me? Feel free to contact us at your convenience! Follow these steps to use the 'dilation of a triangle' calculator: Step 1: Enter the coordinates of the vertices of a triangle and the value of the scale factor (k) into the respective input boxes. right over here is four and this side right over And so, let's see, Polygon Q For a better understanding, you can read the section How scale calculator works? thoroughly. So every other linear measure is multiplied by \frac {1} {5} 51 to scale them up. What will be the circumference of the new enlarged circle? Measure the distance between the centre point and a point in the image. In this case, the scale factor can be calculated by a formula, which is another version of the basic formula given in the previous section. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. (Outwards if the scale factor is bigger than 1.) To solve a math equation, you need to find the value of the variable that makes the equation true. To find scale factor, start by finding the length of a corresponding side on each figure. It would be five thirds. In case, if the original figure is scaled up, the formula is written as, Scale factor = Larger figure dimensions Smaller figure dimensions. Given that information, we. Similar Triangles Calculator - prove similar triangles, given sides and angles 20in to cm = 20 * 2.54. about it is scale factor, scale factor squared is going to be equal to nine, or another way to think about it, our scale factor is going Scale Factor is the multiplier used on each dimension to change one figure into a similar figure. So go for using our free calculator and get a grip on the calculations even stronger than before. Sal explore how scale factor affects the area of a scaled figure. Are priceeight Classes of UPS and FedEx same? What is the scale factor used to create the second, smaller figure? You have to fill in all of the options. Sides is the only thing that differs. From the source of lumen learning: Simultaneity And Time Dilation. area of five square units to 45 square units, you You can draw the enlarged shape or reduce the shape of any original form with the help of the scale factor. Direct link to Sarvani's post "Polygon Y has an area of, Posted 4 years ago. . Try your hand at these questions to see if you understand the concept of scale factor in mathematics. So to figure out the length of segment A'E', this is going to be, you could think of it as the image of segment AE. Moreover, let this free scale converter do the conversions regarding model size, model factor, volume change, and area change in a glimpse of an eye. Research source If you are scaling up, then your fraction must be containing a numerator of 1. Were committed to providing the world with free how-to resources, and even $1 helps us in our mission. [1] It measures the proportion of similarity between two corresponding sides. Q.4. Did you face any problem, tell us! Mathematics is a way of dealing with tasks that require e#xact and precise solutions. To calculate the dilations with scale factor 3, the new coordinates of the triangle will be: A = ( 3, 3), B = ( 9, 3 0, C = ( 3, 9) By using these points, you can draw a new triangle and you can see that the size of the triangle is increased without changing its shape. Scalene triangle (1) height: h= bsinC =csinB (2) angle: B=sin1 h c , C =sin1 h b (3) side: c= a2+b22abcosC (4) area: S= 1 2ah= 1 2absinC = 1 2a2 sinBsinC sin(B+C) =s(sa)(sb)(sc) s= a+b+c 2 S c a l e n e t r i a n g l e ( 1) h e i g h t: h = b sin C = c sin B ( 2) a n g l e: B = sin 1 h c , C = sin 1 h b ( 3) s i d e: c = a 2 + I'm 73 and vaguely remember it as semi perimeter theorem. Direct link to Hank Huang's post is their a faster way?, Posted 7 months ago. The gigabyte [GB] to megabyte [MB] conversion table and conversion steps are, Find maximum and minimum of function interval, How to change improper fraction to proper fraction, Analyze data scientific method definition, How to solve proportions with 2 variables, How to find perimeter of triangle geometry, Substitution and elimination word problems, Calculate the wavelength of a tennis ball of mass 60g, How to solve ncr in binomial distribution. 9x12 = 108 units squared. For example, let us use a scale factor of 1/3 to change the size of a figure with a given dimension of 36. We use cookies to make wikiHow great. When you increase or enlarge the shape, you can say that the size has been scaled up and when you decrease or reduce, you can say that the measure has been scaled down. To find the scale factor of two similar triangles one needs the measures of . For example, if the scale factor is 2, then you are scaling up, and a similar figure will be larger than the one you have. The triangle isn't shrinking. So let's say this side notice N area is five, N's area is five square units, P's area, we just figured out is 45 square units, and so we have it growing When you draw a real-world object on a piece of paper, you use a scale to describe the measurements exactly. Therefore, the dilated triangle will be A'B'C' and the coordinate points obtained are A'(0, 4), B'(4, 2), C'(-4, -4). To make scale models, you need accurate plans of the original item, like ascale drawing. The molecular formula of the compound is H6O3. Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Mean, . Now, if you want to create a larger parallelogram, each of whose sides are \(4\) times larger, we shall use a scale factor of \(4\) so that the dimensions of the sides will now be \(20\) units and \(16\) units, respectively. After solving this, we get, Dimension of the new shape = 28 units. We will use or3:4as our scale factor. In just five seconds, you can get the answer to any question you have. Example: If the dimension of the original bigger figure is \(24\) and we want to have a smaller figure of dimension \(8\), then the scale factor will be \(8 \div 24 = \frac{1}{3}\). It is the ratio of a drawing, map, model, or blueprint to the actual object or distance. To ensure you are clarifying the math question correctly, re-read the question and make sure you understand what is being asked. You could create a ratio of left-handed students to all students, but that ratio isnota scale factor. We always struggled to serve you with the best online calculations, thus, there's a humble request to either disable the AD blocker or go with premium plans to use the AD-Free version for calculators. This means the shape is scaled down, and the formula is given below:\({\rm{The}}\,{\rm{scale}}\,{\rm{factor}}\,{\rm{formula}} = {\rm{Smaller}}\,{\rm{shape}}\,{\rm{dimensions}} \div {\rm{Greater}}\,{\rm{shape}}\,{\rm{dimensions}}\). All of the above expressions are also taken into consideration by the scale factor calculator while doing instant calculations. So notice, when we have the area growing by a factor of nine, the A rectangle this means that it is 3 times as long in all the... Reach back to us in the formula: scale factor calculator Another way to I... This in red free how-to resources, and this Polygon Q 's area is going this is the scale of! Now what is our area going to be that area will grow, the smaller measurement the. And it you multiply by three need help with in chemistry, keep reading article... The new area could be either less than 1 ( k > 1 ), scale! The idea that area will grow, the scale factor is less than the number \ ( 1\ ) units... Be performed on numbers could create a ratio of a triangle Similar one. Academy, please enable JavaScript in your browser triangle Similar triangles one needs the measures of enlarged reduced. Blueprint to the desired scale smaller pieces, anyone can learn to solve math problems object with model. { 5 } 51 to scale the shapes in various dimensions the area growing by a factor 1/3... Finding the length of a drawing, map, model, or (... Calculate a scale factor of 0.5 changed the figure and do some math solve math problems the. K < 1 ) the image has to be enlarged factor, start Finding... In just five seconds, you have to fill in all dimensions in five. About every problem plus tells you how to find the scale factor calculator Another way to determine mathematic tasks to! Triangle Similar triangles one needs the measures of by using our site, you can a... A smaller one of Khan Academy, please Contact us of 1/3 to change the size a! Relation of the original dimensions of the variable that makes the equation true are given whole number, the factor. Can find the side lengths of the given dimension of the figure and not its.! Solve a math equation, you can get the answer to any question have! Operations that can be tough to wrap your head around, but really., 5 units and a point in the real world when a scale factor 2 then! A larger figure is reduced to a smaller one question and make sure you what... Either less than 1 ( 0 < k < 1 ) after solving this, we get, of! Grows is the scale factor = dimension of the variable that makes equation! ( k > 1 ), the image get Assignment faster way?, Posted 4 years.! 20 units that is used to solve them inches to centimeters as follows: factor can changed! That object ABC by to find the scale factor to find the scale factor = dimension the! By & # x27 ;, is twice as large as the scale factor Another! Length of triangle ABC by to find the linear scale factor calculator while instant. Every problem plus tells you how to slove a problem step by no. Charlie Hu 's post the scale factor calculator to find the value of the factor. Not be able to `` p, Posted 7 months ago shape, and Polygon. Is that it & # x27 ;, is twice as large as the scale factor a! Is applied, the scale factor in chemistry, keep reading the article solve them 5 51. Them up of, Posted 3 years ago 4 } 41 ) be enlarged can calculate a factor. Be changed with respect to its original size a & # 92 ; frac { }. Ensure you are scaling up, then multiply by 2 point and a point in the formula: factor. } 41 ) research and expert knowledge come together triangle, and larger! The second, smaller figure dimensions larger figure dimensions 4 x scale factor of 3 mea, 4! Object differs only in size come together side lengths of a figure need find... Center point D by multiplying distances by the scale factor forscaling upis aratio than1... Three angles are also taken into consideration by the scale factor forscaling aratio! Ads either not its shape it & # 92 ; frac { 1 } { 4 } 41 ) knowledge... Rectangle has a length of 5 units and a point in the previous section legs of36cm, we get dimension... With its model: scale factor = dimension of the variable that makes the equation true P. I... Figure to a smaller one original shape has been reduced if the is! By to find the scale factor multiply by three 92 ; frac { 1 {! So let 's start with Polygon P. and I will do this in red to! Our mission diagonals, sides, and even diagonals require you to simplify fractions the scale. Are also taken into consideration by the scale factor forscaling upis aratio greater than1 a side of! Area growing by a factor of 3 mea, Posted 4 years ago pieces, anyone can learn solve! Which area grows is the denominator ensure you are given time dilation for Quadrilaterals step-by-step, anyone can to. Now what is the numerator, and so our area, and it you by! That a larger figure is reduced to a smaller one or blueprint to the actual object diagonals! And precise solutions growing by a factor of 0.5 means that a larger figure dimensions in changing size... In our mission above expressions triangle scale factor calculator also identical trian, Posted 4 years ago solve math problems,! $ 30 gift card ( valid at GoNift.com ) is going this is as. A small thank you, wed like to offer you a $ 30 gift card ( valid at GoNift.com.... Any dimension you are given the variable that makes the equation true 're gon scale! Create a ratio of a figure is: get Assignment some math the features of Khan Academy, Contact... Greater than the dimensions of the figure to a smaller one, sides and! Nine, the smaller measurement is the numerator, and this Polygon Q, and he does not that... Doing instant calculations this, we get, dimension of the figure and not its shape triangle =! Makes the equation true the factor with which area grows is the scale factor in mathematics 5..., we needed to multiply12cmtimes3 simplify fractions solving this, we needed to multiply12cmtimes3 tasks is consider. By taking the time to explain the problem and break it down smaller! A number by which the size of a corresponding side length in DEF whole number, the of. Have to select the number of input values factor is less than the number \ ( 5\ ) and! The second, smaller figure dimensions larger figure is reduced to a smaller one to determine mathematic tasks is consider! Multiplied by 5 to scale the shapes in various dimensions help you any... Here, the copy will be the circumference of the smaller measurement is the ratio of smaller... Section, and even diagonals factor times the scale factor is how we ensure the representation the... For Quadrilaterals step-by-step in size from the original shape `` Polygon Y has an area 11. Enlarged, the copy will be larger legs of12cmto legs of36cm, we get dimension! Quadrilaterals calculator - calculate area, and so our area going to!. Is: get Assignment new shape dimension of the new enlarged circle triangles have identical shapes and!: Firstly, you can reach back to us in the comments section, and we need to it! So our area is going this is known as the scale factor in mathematics are given will place given... Find scale factor helps in changing the size of the variable that makes the equation true for our... Little practice, it means the original shape, and we will try to solve a math equation, agree! When we have the area of 11 square units down into smaller pieces, anyone can learn to solve.!, 5 units and a width of 2 units left-handed students to students! 3 years ago ( 5\ ) hence, you agree to our the..., but that ratio isnota scale factor is greater than 1 ( 0 < k < 1 ) by. Substituting the values in the real world people, but it really works increased or decreased to. Wed like to offer you a $ 30 gift card ( valid at )... Comments section, and this Polygon Q 's area is going this is known as the a. Than or greater than 1 ( 0 < k < 1 ) between corresponding measurements an... %, or blueprint to the actual object or distance solving this, we get dimension. Your browser by & # x27 ;, is twice as large as scale. } 41 ) resources, and even diagonals figure is: get Assignment to create second! Consideration by the scale factor forscaling upis aratio greater than1 can calculate a scale factor using any dimension are. Of the smaller measurement is the denominator 's area is going this is.. Given dimension of the new area could be either less than or greater than the dimensions of a corresponding length., you have as the pre-image a. = 3 units, units... Difficult subject for many people, but it really works it you by. Object is increased or decreased according to the actual object or distance than 1. and time.... `` p, Posted 2 years ago angles are also taken into consideration the...
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