Question

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

sin (A+ B) = `sqrt3/2 and cos 2A = 1/2`

Answer 1

Given:

sin (A + B) = `sqrt3/2`, cos 2A = `1/2`,   ...[A, B Acute]

Step 1: Find A

Since A is acute → 0° < 2A < 180°

cos x = `1/2` in this range at x = 60°

2A = 60° = A = 30°

Step 2: use sin (A + B) = `sqrt3/2`

sin(A + B) = `sqrt3/2` = A + B = 60° or 120°

A = 30° 

A + B = 60° = B = 30° acute

A + B = 120° = B = 90°, not acute