Question

In a right triangle, the acute angles have the relationship sin(x+12°)=cos(18°+2x)
. What is the value of x? What is the measure of the smaller angle? Use 1–2 sentences to explain how you arrived at your answers.(2 points)

Answer 1

x = 20°. Then the acute angles are x+12 = 32° and 18+2x = 58°, so the smaller angle is 32°.

Explanation: cos(18+2x)=sin(90°-(18+2x))=sin(72-2x), so sin(x+12)=sin(72-2x) ⇒ x+12=72-2x ⇒ 3x=60 ⇒ x=20°.