Strategy #15: Use Special Right Triangle Ratios

Category: Geometry

30-60-90 triangle sides are in ratio 1 : √3 : 2 (short leg : long leg : hypotenuse).

45-45-90 triangle sides are in ratio 1 : 1 : √2 (leg : leg : hypotenuse).

Why it matters: These triangles appear constantly in SAT geometry problems. Recognizing them immediately lets you find missing sides without using the Pythagorean theorem.

Example: In a 30-60-90 triangle with hypotenuse 10, the short leg is 5 and the long leg is 5√3.

Practice tip: When you see a right triangle with a 30°, 60°, or 45° angle labeled, immediately write out the ratio. Scale it to match the given side.

Here’s an example: