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.
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.
Trig ratios are used to find missing side lengths and angles of special right triangles. See a summary of trig functions below.
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.
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.