To find the area of triangle \( ABC \) using the formula
\[ A = \frac{1}{2}ab \sin C, \]
we will substitute \( a = 16 \) inches, \( b = 18 \) inches, and \( \angle C = 43^\circ \).
First, we calculate \( \sin C \):
\[ \sin 43^\circ \approx 0.681998. \]
Now, substitute the values into the area formula:
\[ A = \frac{1}{2} \times 16 \times 18 \times \sin(43^\circ). \]
Calculating this step-by-step:
- Calculate \( \frac{1}{2} \times 16 \):
\[ \frac{1}{2} \times 16 = 8. \]
- Calculate \( 8 \times 18 \):
\[ 8 \times 18 = 144. \]
- Now multiply by \( \sin(43^\circ) \):
\[ A = 144 \times 0.681998 \approx 98.081. \]
To the nearest square inch, the area \( A \) is approximately \( 98 \) square inches.
The correct response is:
98 inches²