Question

Consider △ABC.

Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 13, the length of B C is 12, and the length of A C is 5.
What are the angles that make the trigonometric statements true?

sin(
) = cos(B)

sin(B) = cos(
)

Answer 1

Since ∠C = 90°, ∠A + ∠B = 90°, so A and B are complementary. Hence
- sin(A) = cos(B) (numerically sin A = 12/13 = cos B = 12/13),
- sin(B) = cos(A) (numerically sin B = 5/13 = cos A = 5/13).

So the blanks are A in both cases:
sin(A) = cos(B) and sin(B) = cos(A).