Question

Angles ∝ 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 > ∝. sin( x/2 + 20) = cos(2x - 25/2 )

A)
25°


B)
33°


C)
36.5°

D)
53.5°

Answer 1

53.5°

Sine and cosine of complementary angles. Thus,

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

`x = 33`

then,

`(33)/(2) + 20` →
`x= 36.5`

`2(33) - (25)/(2)` →
`x = 53.5`

thus,

β
`= 53.5`

Answer 2

The answer is D: 53.5