Question

Find the area of the triangle if b=13
inches, c=9
inches, and α=25°
. Round to the nearest tenth.

Answer 1

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

\[
\text{Area} = \frac{1}{2} \times b \times c \times \sin(\alpha)
\]

where:
- \( b = 13 \) inches
- \( c = 9 \) inches
- \( \alpha = 25^\circ \)

First, we need to calculate \(\sin(25^\circ)\). Using a calculator:

\[
\sin(25^\circ) \approx 0.4226
\]

Now we can substitute the values into the area formula:

\[
\text{Area} = \frac{1}{2} \times 13 \times 9 \times \sin(25^\circ)
\]
\[
\text{Area} = \frac{1}{2} \times 13 \times 9 \times 0.4226
\]
\[
\text{Area} = \frac{1}{2} \times 117 \times 0.4226
\]
\[
\text{Area} = 58.5 \times 0.4226 \approx 24.7361
\]

Rounding to the nearest tenth:

\[
\text{Area} \approx 24.7 \text{ square inches}
\]

Thus, the area of the triangle is approximately \( \boxed{24.7} \) square inches.