Final answer:
Using the cosine function, ∠R of ΔRST is found by dividing the length of ST by RS and taking the inverse cosine. After calculations, ∠R is approximately 37.5°, which rounds to 37°, indicating that the provided options may be incorrect.
Step-by-step explanation:
To find the measure of ∠R in ΔRST where ∠T=90°, ST = 7.7 feet, and RS = 9.7 feet, we will use the trigonometric function of sine, cos or tan, as it is a right triangle. However, since RS is the hypotenuse, it makes more sense to use the cosine function for ∠R because we know the adjacent side (ST) and the hypotenuse (RS).
The cosine of an angle in a right triangle is equal to the adjacent side divided by the hypotenuse, that is:
cos(∠R) = ST / RS
∠R = cos¹ (ST / RS)
By substituting the given lengths:
∠R = cos¹ (7.7 / 9.7)
When you calculate this using a calculator, make sure it is set to degree mode. After calculation, you get:
∠R ≈ cos¹(0.793814432)
After calculating the above expression, we find that ∠R = 37.5°, which rounded to the nearest degree is 37°. This means that none of the options a) 44°, b) 46°, c) 47°, d) 49° are correct. There might be a mistake in the question or the options provided.