Question

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 degrees. It is not a right triangle.

86 degrees
27 degrees
7 degrees
1 degrees

Answer 1

To find angle \( C \) using the law of sines, we start with the law of sines formula:

\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]

We know the following:

- \( B = 94^\circ \)
- \( b = 13 \) inches
- \( c = 6 \) inches

First, we apply the law of sines to find the sine of angle \( C \):

\[
\frac{c}{\sin C} = \frac{b}{\sin B}
\]

Plugging in the values we have:

\[
\frac{6}{\sin C} = \frac{13}{\sin(94^\circ)}
\]

Now we need to calculate \( \sin(94^\circ) \). Using a calculator:

\[
\sin(94^\circ) \approx 0.998
\]

Now substituting this value back into the equation:

\[
\frac{6}{\sin C} = \frac{13}{0.998}
\]

To isolate \( \sin C \):

\[
\sin C = \frac{6 \cdot 0.998}{13}
\]
\[
\sin C \approx \frac{5.988}{13} \approx 0.461
\]

Next, we find angle \( C \) by taking the arcsine:

\[
C \approx \arcsin(0.461) \approx 27.45^\circ
\]

Rounding to the nearest degree gives us:

\[
C \approx 27^\circ
\]

Thus, the measure of angle \( C \) is \( \boxed{27} \) degrees.