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

We know that
in a right triangle
if sin A= cos B
then
angle A and angle B are complementary angles
so A+B=90

therefore

(2x-8)+(6x-6)=90-------> 8x-14=90----> 8x=104--------> x=13°

(2x-8)-----> 2*13-8----> 18°
(6x-6)-----> 6*13-6----> 72°
if α < β
then
 α =18°
 β=72°