What is the length of the longer leg of a 30 60 90 triangle with a hypotenuse of length 24 square root of 3

Question

What is the length of the longer leg of a 30 60 90 triangle with a hypotenuse of length 24 square root of 3

Answer 1

In a 30-60-90 triangle, if the shortest side (the side opposite the 30° angle) has length x, then the side opposite the 60° angle has length √3 x and the length of the hypotenuse is 2x.

So, if the hypotenuse has length 24√3, then the shorter leg has length (1/2)(24√3) = 12√3.

Thus, the longer leg has length √3(12√3) = 36

Answer 2

length of hypotenuse = 2

----------------------------- -------

length of longer leg sqrt(3)

substitute given length of hypotenuse and solve for length of longer leg (opposite 60 degree angle)