Question

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 17.2 cm2 17 point 2 cm squared 13.8 cm2 13 point 8 cm squared 14.5 cm2 14 point 5 cm squared 10 cm2. short awnsers pls

Answer 1

To find the area of the triangle, you can use the formula:

\[
\text{Area} = \frac{1}{2}ab \sin(C)
\]

Where:
- \(a = 9 \, \text{cm}\)
- \(b = 5 \, \text{cm}\)
- \(C = 40^\circ\)

First, calculate \(\sin(40^\circ)\):

\[
\sin(40^\circ) \approx 0.6428
\]

Now plug in the values:

\[
\text{Area} = \frac{1}{2} \times 9 \times 5 \times 0.6428 \approx \frac{1}{2} \times 45 \times 0.6428 \approx 22.926 \quad \text{cm}^2
\]

Now divide by 2:

\[
\text{Area} \approx 11.463 \quad \text{cm}^2
\]

Round to the nearest tenth:

\[
\text{Area} \approx 11.5 \quad \text{cm}^2
\]

Among the options provided, none directly match this calculated area. Please verify the parameters, but based on the calculations, the area of the triangle is approximately:

**11.5 cm²**.