Math
Special right triangles.
Definition
Right triangles with angle measures of 30-60-90 or 45-45-90 whose side ratios are fixed. These ratios allow you to find side lengths without a calculator. In a 45-45-90 triangle the sides are in ratio 1:1:√2, and in a 30-60-90 triangle the sides are 1:√3:2.
Examples
Real-world.
- 1 A 45-45-90 triangle with legs of 5 has hypotenuse 5√2
- 2 A 30-60-90 triangle with short leg 4 has long leg 4√3 and hypotenuse 8
- 3 The diagonal of a square creates two 45-45-90 triangles
Key Fact
45-45-90 → 1:1:√2; 30-60-90 → 1:√3:2