Question

For the acute angles in a right triangle, sin(2x)=cos(4x+12°)
sin
⁡
(
2
𝑥
)
=
cos
⁡
(
4
𝑥
+
12
°
)
. What is the measure of the larger angle?

Answer 1

cos(θ) = sin(90° − θ). Since 2x and 4x+12° are acute, set
2x = 90° − (4x + 12°) → 6x = 78° → x = 13°.

The larger acute angle is 4x + 12° = 4(13°) + 12° = 64°.