Answer: The two angles are 30 degrees and 90 degrees.
Explanation:
To answer the question, we can use the trigonometric identity that relates the cosine of an angle to the sine of its complementary angle. The identity is cos(x) = sin(90° - x), where x is an angle in degrees.
In this case, we are given that cos(x) = sin(60°), which means that x and (90° - x) are complementary angles. Therefore, we can write:
x = 90° - 60° = 30°
So one of the angles is 30 degrees. To find the other angle, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Let's call the second angle y. Then we have:
x + y + 60° = 180°
Substituting x = 30°, we get:
30° + y + 60° = 180°
Simplifying, we get:
y = 90°