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.
7 degrees
27 degrees
1 degrees
86 degrees
To use the Law of Sines, we can set up the proportion:
sin(B)/b = sin(C)/c
Substituting in the given values:
sin(94°)/13 = sin(C)/6
To solve for sin(C), we can cross-multiply:
6 * sin(94°) = 13 * sin(C)
sin(C) = (6 * sin(94°)) / 13
Using a calculator, we find:
sin(C) ≈ 0.5353
To find the measure of angle C, we can take the inverse sine:
C ≈ sin^(-1)(0.5353)
C ≈ 31.4°
Rounded to the nearest degree, the measure of angle C is 31°.