Elementary Technical Mathematics

Published by Brooks Cole
ISBN 10: 1285199197
ISBN 13: 978-1-28519-919-1

Chapter 13 - Section 13.3 - Using Trigonometric Ratios to Find Sides - Exercise - Page 458: 2


$$a=213.8cm$$ $$c=226.04cm$$

Work Step by Step

To find side a, we can use the trigonometric ratio for tangent $tanB=\frac{b}{a}$ Where $B=19.0°$ $b=73.6cm$ Solving for b we get: $a=\frac{b}{tanB}$ $a=\frac{73.6cm}{tan(19°)}$ $a=\frac{73.6cm}{0.3443}$ $a=213.8cm$ To find side c (the hypotenuse), we can use the trigonometric ratio for sine. $sinB=\frac{b}{c}$ Where $B=19°$ $b=73.6cm$ Solving for c we get: $c=\frac{b}{sinB}$ $c=\frac{73.6cm}{sin(19°)}$ $c=\frac{73.6cm}{0.3256}$ $c=226.04cm$
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