Special Right Triangles

Explanation

Special right triangles have fixed side ratios:

1. 45°–45°–90° triangle

   • Legs are equal

   • Hypotenuse = leg × √2

   • Example: leg 5 → hypotenuse = 5√2

2. 30°–60°–90° triangle

   • Short leg = x, long leg = x√3, hypotenuse = 2x

   • Example: short leg 3 → long leg = 3√3, hypotenuse = 6

These make solving triangles faster without trigonometry.