Question

For the acute angles in a right triangle, sin(2x)=cos(4x+12°)
. What is the measure of the larger angle?(1 point)
° its not 77 or 73

Answer 1

Use cos(θ) = sin(90° − θ). So
sin(2x) = cos(4x + 12°) = sin(90° − (4x + 12°)) = sin(78° − 4x).

Thus sin(2x) = sin(78° − 4x). So either
1) 2x = 78° − 4x + 360k → 6x = 78° + 360k → x = 13° + 60k, or
2) 2x = 180° − (78° − 4x) + 360k → 2x = 102° + 4x + 360k → x = −51° − 180k (no acute solutions).

For acute x (0°<x<90°) we get x = 13° or x = 73°. The other acute angle is 90° − x, so the larger acute angle is:
- If x = 13°, larger = 90° − 13° = 77°.
- If x = 73°, larger = 73°.

Both 73° and 77° satisfy the equation, so there are two possible triangles. If you have extra context that picks one x, tell me and I’ll pick the correct larger angle.