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 α if α < β. sin(2x − 8) = cos(6x − 6)

Answer 1

Answer:

The value of angle α is 18 degree.

Step-by-step explanation:

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

Given equation is

$\sin (2x-8)=\cos (6x-6)$

$\cos (90-(2x-8))=\cos (6x-6)$        $[\because \sin (90-x)=\cos x]$

Equating both sides.

$90-2x+8=6x-6$

$98+6=6x+2x$

$104=8x$

$13=x$

The value of x is 13.

The measure of angles is

$2x-8=2(13)-8=18$

$6x-6=6(13)-6=72$

Since 18<72, therefore the value of angle α is 18 degree.