Geometry and Trigonometry practice question

Answer: A. 3/5

Because angle B is the right angle, AC is the hypotenuse: AC = √(9² + 12²) = √225 = 15. The leg adjacent to angle A is AB = 9, so cos A = adjacent/hypotenuse = 9/15 = 3/5. Choice B is sin A = BC/AC = 12/15 = 4/5, from using the opposite leg instead of the adjacent leg. Choice D is tan A = 12/9 = 4/3, from using opposite/adjacent instead of adjacent/hypotenuse. Choice C is 9/12, the ratio of the two legs with adjacent placed over opposite (cot A), from dividing by the wrong side.

Why the other answers are wrong

B. 4/5

12/15 = 4/5 uses BC, the leg opposite angle A — that's sin A. Cosine needs the adjacent leg AB, so cos A = 9/15 = 3/5.

C. 3/4

9/12 is the ratio of the two legs (adjacent over opposite), not adjacent over hypotenuse. Cosine's denominator must be the hypotenuse AC = 15, giving 9/15 = 3/5.

D. 4/3

12/9 = 4/3 is opposite/adjacent, which is tan A. For cos A use adjacent/hypotenuse = 9/15 = 3/5.

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