Question

Use the image to answer the question.

A right triangle has three sides with measures. Left leg, 5 point zero. Right leg, 7 point 7. Hypotenuse, 9 point 2. One interior angle is labeled x degrees.

Use the Law of Cosines equation to solve for the indicated angle x. Round your answer to the nearest tenth.

(1 point)
Responses

x=57.1°
x is equal to 57.1 degrees

x=90.3°
x is equal to 90.3 degrees

x=56°
x is equal to 56 degrees

x=32.9°

Answer 1

Use the Law of Cosines with x opposite the 7.7 side:

7.7^2 = 5^2 + 9.2^2 − 2(5)(9.2)cos x
cos x = (5^2 + 9.2^2 − 7.7^2) / (2·5·9.2) = 50.35/92 ≈ 0.5473
x = arccos(0.5473) ≈ 57.1°

Answer: x = 57.1°.