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 cosine formula

For right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$.

Step2: Calculate $\cos C$ in $\triangle ABC$

In right - triangle $ABC$, $\cos C=\frac{BC}{AC}$. Given $BC = 4$ cm and $AC = 5$ cm, so $\cos C=\frac{4}{5}$.

Step3: Calculate $\cos R$ in $\triangle PQR$

In right - triangle $PQR$, $\cos R=\frac{QR}{PR}$. Given $QR = 8$ cm and $PR = 10$ cm, so $\cos R=\frac{8}{10}=\frac{4}{5}$.

Answer:

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