Question

the hypotenuse of the right triangle rst shown is 13 inches long. if the cosine of ∠r is 2/3, about how many inches long is rs, to the nearest tenth? a 5.2 b 6.5 c 9.2 d 12.6 e 32.5

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\angle R\), the adjacent side is \(RS\) and the hypotenuse \(RT = 13\) inches. Given \(\cos\angle R=\frac{2}{5}\).

Step2: Substitute values into the formula

We know that \(\cos\angle R=\frac{RS}{RT}\). Substituting \(RT = 13\) and \(\cos\angle R=\frac{2}{5}\) into the formula, we get \(RS=\cos\angle R\times RT\).

Step3: Calculate the length of \(RS\)

\(RS=\frac{2}{5}\times13=\frac{26}{5}=5.2\)

Answer:

A. 5.2