Question

In a 30-60-90 triangle, the shorter leg has length of 8√3 m. Find the length of the other leg (L) and the hypotenuse (H).

Answer 1

When all of the angles of triangle and one side are known, you can apply the sine law. The shorter leg would correspond to the smallest angle 30. Similarly, the hypotenuse, which is the longest sides, corresponds to 90 degrees. Then the equation would be:

(sin 30 / 8 square root of 3) = (sin 90 / H)
H = 27.71 m

(sin 30 / 8 square root of 3) = (sin 60 / L)
L = 24 m