## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 6 - Review Exercises - Page 798: 20

#### Answer

The two roads measure $404\text{ and }551\text{ feet}$ respectively.

#### Work Step by Step

For the given triangle ABC, $A=55{}^\circ,B=46{}^\circ,a=460$ Using the angle sum property, compute the measure of angle C as follows: \begin{align} & 55{}^\circ +46{}^\circ +C=180{}^\circ \\ & C=180{}^\circ -101{}^\circ \\ & C=79{}^\circ \end{align} Now, using the law of sines we will obtain the value of both b and c: \begin{align} & \frac{a}{\sin A}=\frac{c}{\sin C} \\ & \frac{460}{\sin 55{}^\circ }=\frac{c}{\sin 79{}^\circ } \\ & c\cdot \sin 55{}^\circ =460\cdot \sin 79{}^\circ \\ & c=\frac{460\cdot \sin 79{}^\circ }{\sin 55{}^\circ } \end{align} This gives $c\approx 551$ to the nearest tenth. Also, \begin{align} & \frac{a}{\sin A}=\frac{b}{\sin B} \\ & \frac{460}{\sin 55{}^\circ }=\frac{b}{\sin 46{}^\circ } \\ & b\cdot \sin 55{}^\circ =460\cdot \sin 46{}^\circ \\ & b=\frac{460\cdot \sin 46{}^\circ }{\sin 55{}^\circ } \end{align} This gives $b\approx 404$ to the nearest tenth.

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