Question

In triangle APQR, if the measure of ∠R = 90°, RQ = 5, PR = 12, and QP = 13, what ratio represents the secant of ∠Q?

A. 12/5
B. 13/5
C. 5/12
D. 5/13

Answer 1

B. 13/5, which represents the secant of ∠Q in triangle APQR. This is found by taking the reciprocal of the cosine of ∠Q, which is the ratio of the hypotenuse (13 units) to the adjacent side (5 units).

Step-by-step explanation:

The correct answer is option B. 13/5.

In triangle APQR, we are given that ∠R = 90°, which makes triangle APQR a right triangle with RQ and PR as the legs and QP as the hypotenuse. Since ∠Q is acute in this right triangle, we can determine the trigonometric ratios with respect to it.

The secant of an angle in a right triangle is the reciprocal of the cosine, which is the ratio of the length of the adjacent side to the length of the hypotenuse. In this case, the adjacent side to ∠Q is RQ which measures 5 units, and the hypotenuse QP measures 13 units.

Therefore, the secant of ∠Q (sec Q) is the ratio of the length of the hypotenuse to the length of the adjacent side, which is 13/5.

To find the secant of angle Q in triangle APQR, we need to find the ratio of the hypotenuse (PR) to the adjacent side (QP). The hypotenuse PR = 12 and the adjacent side QP = 13. Therefore, the ratio representing the secant of angle Q is 5/13.