Question

in δrst, the measure of ∠t = 90°, sr = 37, rt = 35, and ts = 12. what is the value of the cosine of ∠r to the nearest hundredth?

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\angle R\), the adjacent side to \(\angle R\) is \(RT\) and the hypotenuse is \(SR\).

Step2: Substitute the values

We know that \(RT = 35\) and \(SR=37\). So, \(\cos R=\frac{RT}{SR}\).
Substitute \(RT = 35\) and \(SR = 37\) into the formula: \(\cos R=\frac{35}{37}\approx0.95\)

Answer:

\(0.95\)