Question

Use the image to answer the question.

Triangle upper A upper B upper C has each of the interior angles by its vertices labeled with singular arcs. Side upper A upper B is labeled c, side upper A upper C is labeled b, and side upper B upper C is labeled a.


Imagine that a is 5 feet, b is 21 feet, and c is 18 feet. If angle B
is 55 degrees, find angle C
. Round your answer to the nearest degree.

(1 point)
degrees

Answer 1

Use the Law of Sines: sin C / c = sin B / b, so

sin C = (c/b) sin B = (18/21) sin 55° = (6/7)·sin 55° ≈ 0.70213.

C = arcsin(0.70213) ≈ 44.6°, which rounds to 45°.

Answer: 45 degrees.