Geometry and TrigonometryVery hardTrigonometric ratios of the two acute angles
Geometry and Trigonometry practice question
Triangle ABC is a right triangle with its right angle at C. If sin A = 5/13, what is the value of cos B?
- A. 5/13Correct
- B. 12/13
- C. 5/12
- D. 13/5
Answer: A. 5/13
Angles A and B are the two acute angles of a right triangle, so they are complementary. The side opposite A is the side adjacent to B, and both ratios divide by the same hypotenuse — so cos B = sin A = 5/13.
Why the other answers are wrong
- B. 12/13
- 12/13 is cos A (and sin B). The question asks for cos B, which uses the side ADJACENT to B — the same side that is opposite A.
- C. 5/12
- 5/12 is tan A. Cosine divides by the hypotenuse, 13, not by the other leg.
- D. 13/5
- 13/5 is the ratio inverted. No sine or cosine of an acute angle can exceed 1.
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