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 β if β < α. sin(7x − 15) = cos(3x + 5)

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
(7x-15)+(3x+5)=90-----> 10x-10=90----> 10x=100----> x=10°
so
7x-15------> 7*10-15----> 55°
3x+5------> 3*10+5----> 35°

we know that
β < α
therefore

the answer is
β =35°