Question

In a right triangle, the acute angles have the relationship sin(x+12°)=cos(18°+2x)
sin
⁡
(
𝑥
+
12
°
)
=
cos
⁡
(
18
°
+
2
𝑥
)
. 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) basic and simple

Answer 1

sin(x+12°)=cos(18°+2x)=sin(90°-(18°+2x)) so x+12°=90°-18°-2x ⇒ 3x=60° ⇒ x=20°.
The acute angles are 20°+12°=32° and 18°+2·20°=58°, so the smaller angle is 32°.