Special Right Triangles

45°-45°-90° Triangle

An isosceles right Triangle. If each leg = a, then:

• Hypotenuse = a√2
• Leg = hypotenuse / √2 = hypotenuse × √2 / 2

Ratio of sides: 1 : 1 : √2

30°-60°-90° Triangle

Half of an Equilateral Triangle. If the short leg (opposite 30°) = a, then:

• Long leg (opposite 60°) = a√3
• Hypotenuse (opposite 90°) = 2a

Ratio of sides: 1 : √3 : 2

Memory Tip

• 45-45-90: Two equal legs, hypotenuse is leg × √2.
• 30-60-90: Short leg × 2 = hypotenuse, short leg × √3 = long leg.