Question

If sin (A + 2B) = 2 cos 60° and A = 3B, find the measures of A and B.

Answer 1

Given,

sin (A + 2B) = 2 cos 60° and A = 3B

sin (A + 2B) = `2 xx 1/2`

sin (A + 2B) = 1 = sin 90°   ...(i)

Put A = 3B in (i), we get

sin (3B + 2B) = sin 90°

sin 5B = sin 90°

⇒ 5B = 90°

⇒ B = `90^circ/5`

∴ B = 18°

⇒ A = 3 × 18°

∴ A = 54°