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

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 \( \boxed{14.5 \, \text{cm}^2} \).
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