Special Right Triangles

Hey,

I'm in need for some assistance, on answering this questio,

The hypotenuse of a 30 – 60- 90 right triangle measure 18cm. What are the lengths of the longer leg and shorter leg?

30 degrees -> Pi/6 rad
60 degrees -> Pi/3 rad

Shorter leg = 18*sin(Pi/6) = 18*cos(Pi/3) = 9 cm
Longer leg = 18*cos(Pi/6) = 18*sin(Pi/3) = 9*sqrt(3) cm

You can also use the fact that 30-60-90 triangles always have a shorter leg that's exactly half the length of the hypotenuse.

So:
Shorter leg = 9 cm
Longer leg = sqrt(18^2 - 9^2) = sqrt(324 - 81) = sqrt(243) = sqrt(81)*sqrt(3) = 9*sqrt(3) cm