To find angle \( C \) using the Law of Sines, we start with the formula:
\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]
Given:
- \( B = 94^\circ \)
- \( b = 13 \) inches
- \( c = 6 \) inches
We first need to find angle \( A \) using the Law of Sines. We can express it as:
\[ \frac{b}{\sin B} = \frac{c}{\sin C} \]
We can rearrange this to express \( \sin C \):
\[ \sin C = \frac{c \cdot \sin B}{b} \]
Substituting the known values:
\[ \sin C = \frac{6 \cdot \sin(94^\circ)}{13} \]
Now, calculate \( \sin(94^\circ) \):
\[ \sin(94^\circ) \approx 0.998 \]
Now substitute \( \sin(94^\circ) \) back into the equation:
\[ \sin C = \frac{6 \cdot 0.998}{13} \approx \frac{5.988}{13} \approx 0.461 \]
Now, we will calculate angle \( C \):
\[ C = \arcsin(0.461) \]
Using a calculator:
\[ C \approx 27.5^\circ \]
Rounding to the nearest degree:
\[ C \approx 28^\circ \]
However, since 28 degrees is not one of the response options, it seems we have a mismatch. The closest reasonable option to our answer within the options provided is 27 degrees.
Therefore, the final answer is:
27 degrees
28 answers