Question

Find the area of the triangle if a=9
inches, b=8
inches, and α=30°
. Round 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:

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

where \( a \) and \( b \) are the lengths of the sides and \( \alpha \) is the angle between them. In this case, you have:

- \( a = 9 \) inches
- \( b = 8 \) inches
- \( \alpha = 30^\circ \)

First, we need to calculate \( \sin(30^\circ) \):

\[
\sin(30^\circ) = \frac{1}{2}
\]

Now, substitute the values into the area formula:

\[
\text{Area} = \frac{1}{2} \times 9 \times 8 \times \sin(30^\circ)
\]

\[
\text{Area} = \frac{1}{2} \times 9 \times 8 \times \frac{1}{2}
\]

\[
\text{Area} = \frac{1}{2} \times 9 \times 8 \times 0.5
\]

\[
\text{Area} = \frac{1}{2} \times 9 \times 4
\]

\[
\text{Area} = \frac{1}{2} \times 36
\]

\[
\text{Area} = 18
\]

Thus, the area of the triangle is:

\[
\boxed{18} \text{ square inches}
\]