Question

Area of Triangles Quick Check 4 of 54 of 5 Items Question Use the image to answer the 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) Responses 196 inches2 196 inches squared 134 inches2 134 inches squared 105 inches2 105 inches squared 98 inches2 98 inches squared Skip to navigation page 14 of 14

Answer 1

To find the area of triangle ABC using the formula \( A = \frac{1}{2}ab\sin(C) \), you can substitute the values given:

- \( a = 16 \) inches
- \( b = 18 \) inches
- \( C = 43 \) degrees

First, calculate \( \sin(43^\circ) \). The approximate value of \( \sin(43^\circ) \) is about 0.682.

Now plug the values into the formula:

\[
A = \frac{1}{2} \times 16 \times 18 \times \sin(43^\circ)
\]
\[
A = \frac{1}{2} \times 16 \times 18 \times 0.682
\]
\[
A = 8 \times 18 \times 0.682
\]
\[
A = 144 \times 0.682 \approx 98.208
\]

Rounding to the nearest square inch gives us:

\[
A \approx 98 \text{ inches}^2
\]

Therefore, the area of triangle ABC is approximately **98 inches²**.