Precalculus (6th Edition) Blitzer

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

Chapter 6 - Section 6.1 - The Law of Sines - Exercise Set - Page 722: 52


The height of the tree is $\text{233}\text{.0 feet}$.

Work Step by Step

By observing the figure, we can find $\begin{align} & C=62{}^\circ +23{}^\circ \\ & =85{}^\circ \end{align}$ To find angle B, we will use the angle sum property: $\begin{align} & B=180{}^\circ -A-C \\ & =180{}^\circ -75{}^\circ -85{}^\circ \\ & =20{}^\circ \end{align}$ Using the law of sines, we will find c: $\begin{align} & \frac{c}{\sin C}=\frac{b}{\sin B} \\ & \frac{c}{\sin 85{}^\circ }=\frac{80}{\sin 20{}^\circ } \\ & c=\frac{80\sin 85{}^\circ }{\sin 20{}^\circ } \\ & \approx 233.0 \end{align}$ Therefore, the height of the tree is $\text{233}\text{.0 feet}$.
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