Given a right triangle, which of the following is equal to $\sin (38°)$?

• A. $\tan (52°)$
• B. $\tan (38°)$
• C. $\cos (52°)$
• D. $\cos (38°)$

Answer: (C)

Verified step by step guidance

1. Recall that in a right triangle, the two non-right angles are complementary, meaning their measures add up to 90°. So, if one angle is 38°, the other must be 90° - 38° = 52°.
2. Understand the relationship between sine and cosine for complementary angles: \(\sin(\theta) = \cos(90^\circ - \theta)\).
3. Apply this identity to the given angle: \(\sin(38^\circ) = \cos(90^\circ - 38^\circ) = \cos(52^\circ)\).
4. Recognize that this means \(\sin(38^\circ)\) is equal to \(\cos(52^\circ)\), which matches one of the given options.
5. Note that tangent functions do not directly equal sine of an angle unless related through other identities, so the correct choice is the cosine of the complementary angle.