Question

1. if △abc~△pqr, which statement describes cos c and cos r? remember: cos = adj/hyp a. the values of the cos of ∠c and the cos of ∠r are equal. b. the value of the cos of ∠c is twice as large as the value of the cos of ∠r. c. the value of the cos of ∠c is 4/5 as large as the value of the cos of ∠r. d. the values of the cos of ∠c and the cos of ∠r cannot be determined with the information provided.

Explanation:

Step1: Recall property of similar triangles

If $\triangle ABC\sim\triangle PQR$, then corresponding angles are equal, i.e., $\angle C=\angle R$.

Step2: Recall cosine - angle relationship

Since $\cos\theta=\frac{\text{adj}}{\text{hyp}}$ and $\angle C = \angle R$, the values of $\cos C$ and $\cos R$ are equal because for equal angles, the ratio of adjacent - side to hypotenuse in right - triangles (or in the context of trigonometric functions) is the same.

Answer:

A. The values of the cos of $\angle C$ and the cos of $\angle R$ are equal.