Answer:
the two acute angles is 46°.
Explanation:
In a right triangle, the sine of an angle is equal to the cosine of its complementary angle. So, if sin (8x + 6)° = cos (9x - 1)°, then (8x + 6)° and (9x - 1)° are complementary angles. This means that their sum is 90°. So, we can write the equation:
(8x + 6)° + (9x - 1)° = 90°
Solving for x, we get:
8x + 6 + 9x - 1 = 90 17x + 5 = 90 17x = 85 x = 5
Substituting x = 5 into either of the original expressions for the angles, we find that one acute angle is (8 * 5 + 6)° = 46° and the other is (9 * 5 - 1)° = 44°