To find the area of triangle ABC using the formula \( A = \frac{1}{2}ab \sin C \), we can plug in the values for \( a \), \( b \), and \( C \).
Given:
- \( a = 16 \) inches
- \( b = 18 \) inches
- \( C = 43^\circ \)
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First, calculate \( \sin C \): \[ \sin(43^\circ) \approx 0.681998 \]
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Now plug the values into the formula: \[ A = \frac{1}{2} \times 16 \times 18 \times \sin(43^\circ) \] \[ A = \frac{1}{2} \times 16 \times 18 \times 0.681998 \]
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Calculate \( \frac{1}{2} \times 16 \times 18 \): \[ \frac{1}{2} \times 16 = 8 \] \[ 8 \times 18 = 144 \]
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Now multiply this by \( \sin(43^\circ) \): \[ A = 144 \times 0.681998 \approx 98.152 \]
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Finally, round the area to the nearest square inch: \[ A \approx 98 \text{ square inches} \]
Thus, the area of triangle ABC is approximately \( \boxed{98} \) square inches.