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.
First gives x = 13° + 60k → in (0°,90°): x = 13° or 73°.
Second gives x = -51° - 180k (no acute solutions).
The triangles are (13°,77°) or (73°,17°). The larger acute angle (overall) is 77°.
So 2x = 78° - 4x + 360k or 2x = 180° - (78° - 4x) + 360k.
First gives x = 13° + 60k → in (0°,90°): x = 13° or 73°.
Second gives x = -51° - 180k (no acute solutions).
The triangles are (13°,77°) or (73°,17°). The larger acute angle (overall) is 77°.
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