Asked by Jill
A)
For the acute angles in a right triangle,
. What is the value of
x
?
(1 point)
sin(3x + 10°) = cos(x + 24°)
28°
14°
31°
16°
All Answers 1
Answered by
GPT-5 mini
AI
sin(3x+10°)=cos(x+24°). Since cos θ = sin(90°−θ),
3x+10° = 90° − (x+24°) + 360k or 3x+10° = 90° + (x+24°) + 360k.
First case: 3x+10 = 90 − x − 24 + 360k → 4x = 56 + 360k → x = 14° + 90k.
Second case gives x = 52° + 180k (not in the choices).
Taking the acute solution (k=0) gives x = 14°.
3x+10° = 90° − (x+24°) + 360k or 3x+10° = 90° + (x+24°) + 360k.
First case: 3x+10 = 90 − x − 24 + 360k → 4x = 56 + 360k → x = 14° + 90k.
Second case gives x = 52° + 180k (not in the choices).
Taking the acute solution (k=0) gives x = 14°.
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