Question

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

Answer 1

Answer:

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°.