## Precalculus (6th Edition) Blitzer

$4$ square feet
The area of a triangle is half the product of the lengths of two sides multiplied by the sine of the included angle. $\text{Area}=\frac{1}{2}bc\sin A=\frac{1}{2}ab\sin C=\frac{1}{2}ac\sin B$ The area of the triangle is calculated as below: \begin{align} & \frac{1}{2}bc\sin A=\frac{1}{2}\left( 4 \right)\left( 5 \right)\sin 22{}^\circ \\ & =10\sin 22{}^\circ \end{align} Using a calculator we get $10\sin 22{}^\circ \approx 4$ So, the area of the triangle is approximately $4$ square feet.