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
(1 point)
Responses
98 inches2
98 inches squared
134 inches2
134 inches squared
105 inches2
105 inches squared
196 inches2
Answers
GPT-4o mini
To find the area of triangle \( ABC \) using the formula
\[
A = \frac{1}{2}ab \sin C,
\]
we will substitute \( a = 16 \) inches, \( b = 18 \) inches, and \( \angle C = 43^\circ \).
First, we calculate \( \sin C \):
\[
\sin 43^\circ \approx 0.681998.
\]
Now, substitute the values into the area formula:
\[
A = \frac{1}{2} \times 16 \times 18 \times \sin(43^\circ).
\]
Calculating this step-by-step:
1. Calculate \( \frac{1}{2} \times 16 \):
\[
\frac{1}{2} \times 16 = 8.
\]
2. Calculate \( 8 \times 18 \):
\[
8 \times 18 = 144.
\]
3. Now multiply by \( \sin(43^\circ) \):
\[
A = 144 \times 0.681998 \approx 98.081.
\]
To the nearest square inch, the area \( A \) is approximately \( 98 \) square inches.
The correct response is:
**98 inches²**
\[
A = \frac{1}{2}ab \sin C,
\]
we will substitute \( a = 16 \) inches, \( b = 18 \) inches, and \( \angle C = 43^\circ \).
First, we calculate \( \sin C \):
\[
\sin 43^\circ \approx 0.681998.
\]
Now, substitute the values into the area formula:
\[
A = \frac{1}{2} \times 16 \times 18 \times \sin(43^\circ).
\]
Calculating this step-by-step:
1. Calculate \( \frac{1}{2} \times 16 \):
\[
\frac{1}{2} \times 16 = 8.
\]
2. Calculate \( 8 \times 18 \):
\[
8 \times 18 = 144.
\]
3. Now multiply by \( \sin(43^\circ) \):
\[
A = 144 \times 0.681998 \approx 98.081.
\]
To the nearest square inch, the area \( A \) is approximately \( 98 \) square inches.
The correct response is:
**98 inches²**