Question

A building lot in a city is shaped as a 30° -60° -90° triangle. The side opposite the 30° angle measures 41 feet.
 
a. Find the length of the side of the lot opposite the 60° angle.
 

b. Find the length of the hypotenuse of the triangular lot.

Answer 1

I will do b first.
b. You know that sin 30 = 1/2. So, sin 30 = 41/hypotenuse. hypotenuse is 82.

a. the length opposite of 60 deg angle is obviously 41√3 because the triangle is in ratio of x : x√3 : 2x (30: 60: 90). This also explains part b.