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The Math section of the SAT is full of special right triangles.
The 5-12-13 triangle is a common triple. If you can recognize the triple pattern then you can easily calculate a missing side. Here is a list of the common triples associated with a 5 -12-13 right triangle.

5-12-13
x2  10-24-26
x3  15-36-39
x4  20-48-52
x5 25-60-65

For example:  If you see a right triangle with a leg of 15 and the hypotenuse is 39, you can divide by 3 to get back to the 5, 12, 13 triangle.  Then you take the leg of 12 and multiply it by 3 to find the missing length, 36, of the larger right triangle.

Common Core Standard F.TF.3  Special Right Triangles

What are special right triangles? They are triangles that have regular patterns which makes calculations of the triangle easier. The following  special right triangles are investigated,
• 30-60-90 triangle
•  45-45-90 triangle
• 3-4-5 triangle
•  5-12-13 triangles.
 45°- 45°- 90° Triangles   A right triangle with two sides of equal lengths is a 45°- 45°- 90° triangle.   The length of the sides are in the ratio of 1:1: √2   Leg length = 1/2 hypotenuse√2   Hypotenuse = leg√2 30°- 60°- 90° Triangles   Hypotenuse is always opposite the right angle   Short Leg is opposite the 30◦ angle   Long leg is opposite the 60◦ angle   The lengths of the sides of a 30°- 60°- 90° triangle are in the ratio of 1: √3 :2   Short leg = ½ hypotenuse   Long leg = 2* short leg   Hypotenuse = √3 * short side 5-12-13 Triangles   A 5-12-13 triangle is a right-angled triangle whose lengths are in the ratio of 5:12:13.   Notice that 5:12:13 satisfies the Pythagorean theorem and is a common triplet. This can be used to identify leg lengths 3-4-5 Triangles   3-4-5 triangles have leg lengths in the ratio of 3:4:5   If the length of the right triangle are in the ratio 3:4:5 then the other leg lengths can be found easily   If you have the following information: A right angle Length of opposite leg Length of the hypotenuse Use Sin   Opposite Hypotenuse A right angle Length of adjacent leg Length of the hypotenuse Use Cosine   Adjacent Hypotenuse A right angle Length of opposite leg Length of the adjacent Use Tangent   Opposite Adjacent Pythagorean theorem and special right triangles

The Pythagorean Theorem can be used to prove that a 5-12-13 and 3-4-5 are right triangles.
The Pythagorean Theorem states that the square of the hypotenuse is equal to the sum of the two sides squared.

3^2 + 4^2 = 5^2
9 + 16 =25
Lets try a 5-12-13 triangle
5^2 + 12^2 = 13^2
25 +144 =169

Special right triangles applications

The 3-4-5 rule to build square corners has been used for years by carpenters to help keep foundations, and buildings square. Using just a saw, and a tape measure, one can create a ninety degree angle, and keep a foundation square. For instance,imagine you are laying a foundation, one can cut a 3, 4, and 5 foot long board. Next, arrange the boards so that they create a triangle in a corner, and a ninety degree angle will be created. This ninety degree angle will keep the foundation square. 3
5
4

Any multiple of 3-4-5 will create a 90 degree angle. Here is a 3-4-5 cheat sheet of the multiples to 80.

3-4-5           15-20-25     27-36-45     39-52-65

6-8-10         18-24-30    30-40-50    42-56-70

9-12-15        21-28-35    33-44-55     45-60-75

12-16-20      24-32-40   36-48-60     48-64-80