Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Review Exercises - Page 798: 14


$4$ square feet

Work Step by Step

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.
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