Question
Use the formula A=12absinC to determine the area of △ABC . What is the area to the nearest square inch if a=16 inches , b=18 inches , and ∠C=43 degrees ?(1 point)Responses196 inches2196 inches squared134 inches2134 inches squared98 inches298 inches squared105 inches2105 inches squared
Answers
GPT-4o mini
To find the area of triangle \( \triangle ABC \) using the formula \( A = \frac{1}{2}ab \sin C \), we can substitute the given values:
- \( a = 16 \) inches
- \( b = 18 \) inches
- \( C = 43^\circ \)
1. First, calculate \( \sin(43^\circ) \). Using a calculator,
\[
\sin(43^\circ) \approx 0.681998
\]
2. Now plug the values into the area formula:
\[
A = \frac{1}{2} \cdot 16 \cdot 18 \cdot \sin(43^\circ)
\]
\[
A \approx \frac{1}{2} \cdot 16 \cdot 18 \cdot 0.681998
\]
\[
A \approx 8 \cdot 18 \cdot 0.681998
\]
\[
A \approx 144 \cdot 0.681998 \approx 98.0 \, \text{square inches}
\]
Thus, the area of triangle \( \triangle ABC \) to the nearest square inch is approximately **98 square inches**.
- \( a = 16 \) inches
- \( b = 18 \) inches
- \( C = 43^\circ \)
1. First, calculate \( \sin(43^\circ) \). Using a calculator,
\[
\sin(43^\circ) \approx 0.681998
\]
2. Now plug the values into the area formula:
\[
A = \frac{1}{2} \cdot 16 \cdot 18 \cdot \sin(43^\circ)
\]
\[
A \approx \frac{1}{2} \cdot 16 \cdot 18 \cdot 0.681998
\]
\[
A \approx 8 \cdot 18 \cdot 0.681998
\]
\[
A \approx 144 \cdot 0.681998 \approx 98.0 \, \text{square inches}
\]
Thus, the area of triangle \( \triangle ABC \) to the nearest square inch is approximately **98 square inches**.