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.

Answer 1

To find the area of a triangle when you have two sides and the included angle, you can use the formula:

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

where:
- \( a = 9 \) cm,
- \( b = 5 \) cm, and
- \( C = 40^\circ \).

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

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

Now plug in the values into the area formula:

\[
\text{Area} = \frac{1}{2} \times 9 \times 5 \times \sin(40^\circ)
\]
\[
\text{Area} = \frac{1}{2} \times 9 \times 5 \times 0.6428
\]
\[
\text{Area} = \frac{1}{2} \times 45 \times 0.6428
\]
\[
\text{Area} = 22.5 \times 0.6428 \approx 14.451
\]

Rounding this to the nearest tenth, we get:

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

Thus, the area of the triangle is \( \boxed{14.5} \) cm².