Question

noah tried to prove that \\( \cos ( \theta ) = \sin ( \theta ) \\) using the following diagram. his proof is not correct.

what is the first mistake in noahs proof?
choose 1 answer:
angles \\( \angle b \\) and \\( \angle c \\) are complementary, not congruent.
noah used the wrong sides in his ratio for \\( \sin ( \theta ) \\).
noah used the wrong sides in his ratio for \\( \cos ( \theta ) \\).
noah substituted a value that wasnt equivalent to the one he replaced.

Explanation:

In a right - triangle, the sum of the two acute angles is \(90^{\circ}\). So, \(\angle B+\angle C = 90^{\circ}\) (they are complementary). The statement \(m\angle B=\theta\) (claiming they are congruent) is wrong. Congruent angles have equal measures, but in a non - isosceles right - triangle, the two acute angles are not equal.

Answer:

A. Angles \(\angle B\) and \(\angle C\) are complementary, not congruent.