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 + 20x) = cos(2x + 15x 2 ) A) 25° B) 28.5° C) 61.5° D) 65°

Answer 1

Just did this problem it is C.

Answer 2

The correct option is C.

Explanation:

Given information: Angles α and β are the two acute angles , β > ∝.

Given equation is

`\sin((x)/(2)+20x)=\cos (2x+(15x)/(2))`

`\cos(90-((x)/(2)+20x))=\cos (2x+(15x)/(2))`
`[\because \sin (90-x)=\cos x]`

Equating both the sides.

`90-(x)/(2)-20x=2x+(15x)/(2)`

`90=2x+(15x)/(2)+(x)/(2)+20x`

`90=22x+(16x)/(2)`

`90=22x+8x`

`90=30x`

`x=3`

The value of angles is

`(x)/(2)+20x=(3)/(2)+20(3)=1.5+60=61.5`

`2x+(15x)/(2)=2(3)+(15(3))/(2)=6+22.5=28.5`

Since 61.5>28.5, therefore the value of β is 61.5. Option C is correct.