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?

A) 0.49
B) 0.71
C) 0.81
D) 0.92

Answer 1

The value of the cosine of angle r in triangle rst is approximately 0.71.

Step-by-step explanation:

To find the value of the cosine of angle ∠r in triangle ∠rst, we first need to find the length of side sr and side rt. Using the Pythagorean theorem, we can find that sr = √(37^2 + 12^2) = 38.91 and rt = √(35^2 + 12^2) = 37.69. Now, we can use the cosine formula:

cos(∠r) = (sr^2 + rt^2 - ts^2) / (2 * sr * rt)

cos(∠r) = (38.91^2 + 37.69^2 - 12^2) / (2 * 38.91 * 37.69)

cos(∠r) = 0.7059 (rounded to the nearest hundredth)