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 98 inches2 98 inches squared 134 inches2 134 inches squared 105 inches2 105 inches squared 196 inches2

Answer 1

To find the area of triangle \( \triangle ABC \) using the formula \( A = \frac{1}{2}ab\sin C \), we will plug in the given values.

Given:
- \( a = 16 \) inches
- \( b = 18 \) inches
- \( C = 43^\circ \)

First, we will calculate \( \sin(43^\circ) \). You can use a calculator to find this:

\[ \sin(43^\circ) \approx 0.681998 \]

Now we can calculate the area using the formula:

\[
A = \frac{1}{2} \times 16 \times 18 \times \sin(43^\circ)
\]

Substituting the values:

\[
A = \frac{1}{2} \times 16 \times 18 \times 0.681998
\]

Calculating \( \frac{1}{2} \times 16 \times 18 \):

\[
= 8 \times 18 = 144
\]

Now multiplying this by \( \sin(43^\circ) \):

\[
A \approx 144 \times 0.681998 \approx 98.147
\]

Now rounding to the nearest square inch gives us:

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

Thus, the area of \( \triangle ABC \) is approximately \( 98 \) square inches.

The correct response is **98 inches²** or **98 inches squared**.