Question

If cos(2/3x+20)°=sin(2x−10)°, find the acute angles of the corresponding right triangle.

A =
B =

Answer 1

A = 40°

B = 50°

Explanation:

If cos A = sin B, then A + B = 90

So, 2x/3 + 20 + 2x - 10 = 90

2x + 60 + 6x - 30 = 270

8x + 30 = 270

8x = 240

x = 30

2x/3 + 20 = 60/3 + 20 = 20 + 20 = 40

2x - 10 = 2(30) - 10 = 60 - 10 = 50 or 90 - 40 = 50