Question

For the acute angles in a right triangle, sin(3x+10°)=cos(x+24°)
. What is the value of x
?(1 point)
Responses

28°

28 degrees

31°

31 degrees

14°

14 degrees

16°

Answer 1

Use cos θ = sin(90° − θ). So
sin(3x+10°) = cos(x+24°) = sin(90° − (x+24°)) = sin(66° − x).

Thus 3x+10° = 66° − x ⇒ 4x = 56° ⇒ x = 14°.

(Other algebraic solutions give non-acute triangle angles, so x = 14° is the valid one.)