Question

A triangle upper A upper B upper C. The edge upper A upper B is labeled c. The edge upper A upper C is labeled b. The edge upper B upper C is labeled a.
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

105 inches2
105 inches squared

134 inches2
134 inches squared

196 inches2
196 inches squared

98 inches2

Answer 1

To find the area of triangle ABC using the formula \( A = \frac{1}{2}ab \sin C \), we can substitute the given values for \( a \), \( b \), and \( \angle C \).

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

First, we need to calculate \( \sin C \):
\[
\sin 43^\circ \approx 0.6820 \quad (\text{using a calculator})
\]

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

Rounding this to the nearest square inch gives us:
\[
A \approx 98 \text{ inches}^2
\]

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