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)Responses13.8 cm213 point 8 cm squared10 cm210 cm squared17.2 cm217 point 2 cm squared14.5 cm2

Answer 1

To find the area of the triangle given two sides and the included angle, we can use the formula:

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

where \( a \) and \( b \) are the lengths of the sides, and \( C \) is the included angle.

Given:
- \( a = 9 \) cm
- \( b = 5 \) cm
- \( C = 40^\circ \)

First, we need to calculate \(\sin(40^\circ)\). Using a calculator, we find that:

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

Now we can substitute the values into the area formula:

\[
\text{Area} = \frac{1}{2} \times 9 \times 5 \times \sin(40^\circ)
\]

Calculating this step by step:

1. Calculate \( \frac{1}{2} \times 9 \times 5 \) = \( 22.5 \)
2. Now, multiply by \( \sin(40^\circ) \):

\[
\text{Area} = 22.5 \times 0.6428 \approx 14.485
\]

Rounding this to the nearest tenth gives:

\[
\text{Area} \approx 14.5 \, \text{cm}^2
\]

Thus, the area of the triangle is \( \boxed{14.5 \, \text{cm}^2} \).