Question

consider triangles abc and pqr shown below. 11. 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 - ratio formula

The formula for cosine of an angle in a right - triangle is $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$.

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

In right - triangle $ABC$, the side adjacent to $\angle C$ is $BC = 4$ cm and the hypotenuse is $AC = 5$ cm. So, $\cos C=\frac{BC}{AC}=\frac{4}{5}$.

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

In right - triangle $PQR$, the side adjacent to $\angle R$ is $QR = 8$ cm and the hypotenuse is $PR = 10$ cm. So, $\cos R=\frac{QR}{PR}=\frac{8}{10}=\frac{4}{5}$.

Answer:

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