Question

In a right triangle, cos

(
8
x
)
∘
(8x)
∘
= sin
(
2
x
−
10
)
∘
(2x−10)
∘
. Find the larger of the triangle’s two acute angles.

Answer 1

80°

Explanation:

You want the larger of two acute angles in a right triangle if their relationship is cos(8x°) = sin(2x-10°).

Complementary angles

The cosine of an acute angle is equal to the sine of its complement. The given relation between the angles means ...

(8x) +(2x -10) = 90 . . . . . the angles are complementary

10x = 100 . . . . . . . . . . . add 10

x = 10 . . . . . . . . . . . . . divide by 10

The two angles are 8·10° = 80° and (2·10 -10)° = 10°.

The larger of the two acute angles is 80°.