The hypotenuse of a 30° - 60° - 90° triangle is 18. Find the lengths of the other sides.

Answer 1

The hypotenuse of a 30 60 90 triangle is 2x

The other two sides are x and x√3

2x = 18

So in can be said x = 9

That is one side the other being 9√3

Answer 2

sin(x) = opposite side / hypotenuse and cos(x) = adjacent side / hypotenuse.

Rearranging this gives us o = h sin(x) and a = h cos(x).

You can pick any angle you want for this. I'll choose 30 degrees.

o = 18 sin(30 deg) = 9

a = 18 cos(30 deg) = 15.59

To show that it works with the other angle:

o = 18 sin(60 deg) = 15.59

a = 18 cos(60 deg) = 9

Alternatively, you could remember sin(30) = 0.5 or cos(60) = 0.5 and calculate one side that way, then use a² = b² + c² where a is the length of the hypotenuse and b and c are the lengths of the sides.