PSAT Math Multiple-Choice Question 714: Answer and Explanation

Question: 714

Which trigonometric expression would give the value of angle X?

• A.
• B.
• C.
• D.

Correct Answer: A

Explanation:

(A) Here we're looking for an angle measure, so we need an inverse trigonometry function. Let's go through the answer choices.

Choice (A) works because sine is the value of the opposite side over the hypotenuse. Side x is opposite of angle X, and side z is the hypotenuse. Thus, would provide the measure of angle X.

Choice (B) doesn't work because side x is opposite of angle X rather than adjacent, so we don't want to use cos^-1.

Choice (C) won't work because we want an inverse trigonometry function rather than a trigonometry function. The output of an inverse trigonometry function is an angle. In contrast, the output of a trigonometry function is the ratio of two sides of a right triangle.

Choice (D) doesn't work because side y is adjacent to angle X, so sin^-1 is not the appropriate inverse trigonometry function to use.