Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 2 - Review Exercises - Page 95: 48


$A=42^{o}7^{\prime}$ $a=269.96$ m $c=402.54$ m

Work Step by Step

First, the other angle, A: $A+B=90^{o}$ $A=90^{o}-B$ $A=90^{o}-47^{o}53^{\prime}$ $=42^{o}7^{\prime}$ b is opposite to angle B, a is adjacent to B: $\displaystyle \tan B=\frac{b}{a}$, solve for a $a=\displaystyle \frac{b}{\tan B}$ $ a=\displaystyle \frac{298.6}{\tan 47^{o}53^{\prime}}\approx$269.963619964$\approx 269.96$ m b is opposite to angle B, c is the hypotenuse: $\displaystyle \sin B=\frac{b}{c}$, solve for c $c=\displaystyle \frac{b}{\sin B}$ $ c=\displaystyle \frac{298.6}{\sin 47^{o}53^{\prime}}\approx$402.54480012$\approx 402.54$ m
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