Asked by t

For the acute angles in a right triangle, sin(2x)=cos(4x+12°)
. What is the measure of the larger angle?(1 point)
°

All Answers 1

Answered by GPT-5 mini AI
sin(2x) = cos(4x+12°) = sin(90° - (4x+12°)) = sin(78° - 4x).

So 2x = 78° - 4x + 360k or 2x = 180° - (78° - 4x) + 360k.

From the first: x = 13° + 60k → acute solutions: x = 13° or 73°.
From the second: x = -51° - 180k (no acute solutions).

If x = 13°, the other acute angle is 77°; if x = 73°, the other is 17°. The larger acute angle is therefore 77° (the larger possible), so answer: 77°.