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: 11


$$b=54.9m$$ $$c=58.4m$$

Work Step by Step

To find side b, we can use the trigonometric ratio for tangent $tanA=\frac{a}{b}$ Where $A=19.75°$ $a=19.72m$ Solving for b we get: $b=\frac{a}{tanA}$ $b=\frac{19.72m}{tan(19.75°)}$ $b=\frac{19.72m}{0.3590}$ $b=54.9m$ To find side c (the hypotenuse), we can use the trigonometric ratio for sine. $sinA=\frac{a}{c}$ Where $A=19.75°$ $a=19.72m$ Solving for c we get: $c=\frac{a}{sinA}$ $c=\frac{19.72m}{sin(19.75°)}$ $c=\frac{19.72m}{0.3379}$ $c=58.4m$
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