Question

Find the measure of angles A and B in the following, where A and B are acute.

2 cos 3B = 1 and sin (A + B) = 1

Answer 1

Given:

2 cos 3B = 1 and sin (A + B) = 1

Step 1: 

2 cos 3B = 1 ⇒ cos 3B = `1/2`

cos x = `1/2` at x = 60°, 300° 

Since 0° < B < 90° = 0° < 3B < 270°, only 3B = 60° fits.

B = `(60°)/3` = 20°

Step 2: Use sin⁡(A + B) = 1

sin (A + B) = 1 ⇒ A + B = 90° (sum of two acute angles < 180°)   

A = 90° − B = 90° − 20° = 70°

A = 70°, B = 20°   ...[since both are acute]