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

Answer:

The correct option is C.

Step-by-step explanation:

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

Given equation is

$\sin(\frac{x}{2}+20x)=\cos (2x+\frac{15x}{2})$

$\cos(90-(\frac{x}{2}+20x))=\cos (2x+\frac{15x}{2})$        $[\because \sin (90-x)=\cos x]$

Equating both the sides.

$90-\frac{x}{2}-20x=2x+\frac{15x}{2}$

$90=2x+\frac{15x}{2}+\frac{x}{2}+20x$

$90=22x+\frac{16x}{2}$

$90=22x+8x$

$90=30x$

$x=3$

The value of angles is

$\frac{x}{2}+20x=\frac{3}{2}+20(3)=1.5+60=61.5$

$2x+\frac{15x}{2}=2(3)+\frac{15(3)}{2}=6+22.5=28.5$

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