The sides of a right triangle follow Pythagorean's Theorem: A2 + B2 = C2, where C is the hypotenuse (the longest side). Here are a couple of special right triangles to keep in mind, as it can save you a lot of time:
- 45o -- A right triangle with the same length sides (A == B) have two 45-degree angles. The ratio of the lengths of the sides are:
- 1 : 1 : SQRT(2) (A : B : C)
- 30-60-90 -- A right triangle with angles 30, 60, and 90 have the following ratios of the lengths of the sides:
- 1 : 2: SQRT(3) (A : B : C)
- 3-4-5 -- A triangle with sides whose lengths have the ratio of 3 : 4 : 5 is a right triangle. This comes in useful if you realize that you have a right triangle, you can determine the unknown length of one side if you know that either:
- The ratio of one side to its hypotenuse is 3 : 5, or
- The ratio of one side to its hypotenuse is 4 : 5, or
- The ratio of two sides is 3 : 4.
- 5-12-13 -- Same as above, but for a triangle with the sides in the ratio of 5 : 12 : 13.