Special Right Triangles (30-60-90 and 45-45-90)

45-45-90 Triangle (isosceles right triangle): Sides in ratio 1 : 1 : sqrt{2} If legs = a, hypotenuse = asqrt{2} 30-60-90 Triangle: Sides in ratio 1 : sqrt{3} : 2 - Side opposite 30° = x (shortest) - Side opposite 60° = xsqrt{3} - Side opposite 90° = 2x (hypotenuse)

Example: A 30-60-90 triangle has hypotenuse 10. Find the other sides.

These ratios are on the SAT reference sheet, but memorizing them saves precious time. Quick trick: in a 30-60-90, the hypotenuse is always DOUBLE the short leg. In a 45-45-90, multiply a leg by sqrt{2} to get the hypotenuse.