Question

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

Answer 1

Solve sin(2x) = cos(4x+12°). Since cos A = sin(90°−A),

sin(2x) = sin(78° − 4x).

Thus 2x = 78° − 4x + 360k or 2x = 180° − (78° − 4x) + 360k.

From the first: 6x = 78° + 360k ⇒ x = 13° or 73° (for k = 0 or 1).
The second gives no acute solutions.

The two possible acute angle pairs are (13°, 77°) and (73°, 17°). The larger acute angle (the answer sought) is 73°.