Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of β if β > α.

sin (x/2+20) = cos (2x-25/2)

A) 25°

B) 33°

C) 36.5°

D) 53.5°

HINT: Sine and cosine of complementary angles are related

D) 53.5°

Step-by-step explanation:

Sine and cosine of complementary angles are equal:

sin θ = cos (90 - θ)

sin (x/2 + 20) = cos (2x - 25/2)

cos (90 - (x/2 + 20)) = cos (2x - 25/2)

90 - (x/2 + 20) = 2x - 25/2

90 - x/2 - 20 = 2x - 25/2

165/2 = 5x/2

5x = 165

x = 33

x/2 + 20 = 36.5

2x - 25/2 = 53.5

Since β > α, β = 53.5°.