Asked by e
Find the area of the triangle if a = 9 cm, b = 5 cm, and ∠C = 40 degrees. Round your answer to the nearest tenth.
(1 point)
Responses
13.8 cm213.8 cm2
17.2 cm217.2 cm2
10 cm210 cm2
14.5 cm214.5 cm2
(1 point)
Responses
13.8 cm213.8 cm2
17.2 cm217.2 cm2
10 cm210 cm2
14.5 cm214.5 cm2
Answers
Answered by
GPT-4o mini
To find the area of a triangle when two sides and the included angle are known, you can use the formula:
\[
\text{Area} = \frac{1}{2}ab \sin(C)
\]
Where:
- \(a\) and \(b\) are the lengths of the two sides.
- \(C\) is the included angle in degrees.
Given:
- \(a = 9 \, \text{cm}\)
- \(b = 5 \, \text{cm}\)
- \(C = 40^\circ\)
Now, let's substitute the values into the formula:
First, we need to calculate \(\sin(40^\circ)\). Using a calculator:
\[
\sin(40^\circ) \approx 0.6428
\]
Now, substitute into the area formula:
\[
\text{Area} = \frac{1}{2} \times 9 \times 5 \times 0.6428
\]
Calculating the multiplication step-by-step:
\[
\text{Area} = \frac{1}{2} \times 45 \times 0.6428
\]
\[
\text{Area} = 22.5 \times 0.6428 \approx 14.485
\]
Rounding to the nearest tenth gives:
\[
\text{Area} \approx 14.5 \, \text{cm}^2
\]
Thus, the area of the triangle is \( \boxed{14.5 \, \text{cm}^2} \).
\[
\text{Area} = \frac{1}{2}ab \sin(C)
\]
Where:
- \(a\) and \(b\) are the lengths of the two sides.
- \(C\) is the included angle in degrees.
Given:
- \(a = 9 \, \text{cm}\)
- \(b = 5 \, \text{cm}\)
- \(C = 40^\circ\)
Now, let's substitute the values into the formula:
First, we need to calculate \(\sin(40^\circ)\). Using a calculator:
\[
\sin(40^\circ) \approx 0.6428
\]
Now, substitute into the area formula:
\[
\text{Area} = \frac{1}{2} \times 9 \times 5 \times 0.6428
\]
Calculating the multiplication step-by-step:
\[
\text{Area} = \frac{1}{2} \times 45 \times 0.6428
\]
\[
\text{Area} = 22.5 \times 0.6428 \approx 14.485
\]
Rounding to the nearest tenth gives:
\[
\text{Area} \approx 14.5 \, \text{cm}^2
\]
Thus, the area of the triangle is \( \boxed{14.5 \, \text{cm}^2} \).
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