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 12 inches and b is 14 inches. If angle A
is 55 degrees, use the Law of Sines to find the measure of angle B
. Round your answer to the nearest degree.

(1 point)
degrees

Answer 1

By the Law of Sines: sin B = (b sin A)/a = (14 sin 55°)/12 ≈ 0.9557.

So B ≈ arcsin(0.9557) ≈ 73°. (The supplementary angle 180°−73° = 107° also satisfies the sine relation, so the two possible angle measures are 73° or 107°; typically the acute solution 73° is used.)