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.
Given angle B is 94 degrees, use the Law of Sines to find the measure of angle C if b=13 inches and c=6 inches. Round your answer to the nearest degree.
(1 point)
Responses
27 degrees
27 degrees
1 degrees
1 degrees
7 degrees
7 degrees
86 degrees
86 degrees
To find the measure of angle C using the Law of Sines, we can use the formula:
sin A / a = sin B / b = sin C / c
We are given that angle B is 94 degrees, b is 13 inches, and c is 6 inches. Plugging in these values, we get:
sin B / b = sin C / c
sin 94 / 13 = sin C / 6
Now, we can solve for sin C:
sin C = (sin 94 / 13) * 6
sin C = 0.7279
Now, we can find the measure of angle C by taking the arcsin of 0.7279:
C = arcsin(0.7279)
C ≈ 47.97 degrees
Rounded to the nearest degree, angle C is approximately 48 degrees.