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 know two sides and the included angle, you 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 angle between them.

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

Now substitute the values into the formula:

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

First, calculate \( \sin(40^\circ) \):
Using a calculator, \( \sin(40^\circ) \approx 0.6428 \).

Now substitute this value into the equation:

\[
\text{Area} = \frac{1}{2} \times 9 \times 5 \times 0.6428
\]
\[
\text{Area} = \frac{1}{2} \times 45 \times 0.6428
\]
\[
\text{Area} = 22.5 \times 0.6428 \approx 14.485
\]

Rounding to the nearest tenth:

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

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