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

98 inches2
98 inches squared

105 inches2

Answer 1

To calculate the area \( A \) of triangle \( ABC \) using the formula \( A = \frac{1}{2} a b \sin C \), we will substitute the given values \( a = 16 \, \text{inches} \), \( b = 18 \, \text{inches} \), and \( \angle C = 43^\circ \).

First, let's find \( \sin 43^\circ \):

Using a calculator:
\[
\sin 43^\circ \approx 0.6820
\]

Now, we can substitute this into the area formula:
\[
A = \frac{1}{2} \times 16 \times 18 \times \sin(43^\circ)
\]
\[
A = \frac{1}{2} \times 16 \times 18 \times 0.6820
\]
\[
A = 8 \times 18 \times 0.6820
\]
\[
A = 144 \times 0.6820
\]
\[
A \approx 98.208
\]

Rounding to the nearest square inch, the area \( A \) is approximately \( 98 \, \text{inches}^2 \).

Thus, the correct response is:
**98 inches²**.