Question

If triangle ABC has a = 14 inches, b = 60 inches, and angle C = 77 degrees, then what is the area in square inches?

Answer 1

To find the area of triangle ABC with sides \( a \), \( b \), and angle \( C \), we can use the formula:

\[
\text{Area} = \frac{1}{2}ab \sin(C)
\]

where \( a \) and \( b \) are the lengths of two sides of the triangle, and \( C \) is the angle between those two sides.

Given:
- \( a = 14 \) inches
- \( b = 60 \) inches
- \( C = 77^\circ \)

First, we need to calculate \( \sin(77^\circ) \). Using a calculator:

\[
\sin(77^\circ) \approx 0.9744
\]

Now, we can substitute the values into the area formula:

\[
\text{Area} = \frac{1}{2} \times 14 \times 60 \times \sin(77^\circ)
\]

\[
\text{Area} = \frac{1}{2} \times 14 \times 60 \times 0.9744
\]

\[
\text{Area} = 7 \times 60 \times 0.9744
\]

\[
\text{Area} = 420 \times 0.9744
\]

\[
\text{Area} \approx 409.848
\]

Therefore, the area of triangle ABC is approximately

\[
\boxed{409.85} \text{ square inches}.
\]