Question

side a b unknown right angle
hypotenuse 6sqrt3
60 and 30 degree angles

Answer 1

This is a 30–60–90 right triangle (angles 30°, 60°, 90°). Ratios of sides are 1 : √3 : 2 (short leg : long leg : hypotenuse).

Given hypotenuse = 6√3:
- short leg (opposite 30°) = hypotenuse / 2 = (6√3)/2 = 3√3
- long leg (opposite 60°) = short leg × √3 = 3√3 × √3 = 9

So the two legs are 3√3 and 9. (If a is opposite 30° then a = 3√3; if b is opposite 60° then b = 9.)