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In ΔRST, the measure of ∠T=90°, ST = 7.7 feet, and RS = 9.7 feet. Find the measure of ∠R to the nearest degree.

a) 44°
b) 46°
c) 47°
d) 49°

1 Answer

5 votes

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.

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