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: 12


$$a=290.4cm$$ $$c=316.3cm$$

Work Step by Step

To find side a, we can use the trigonometric ratio for tangent $tanB=\frac{b}{a}$ Where $B=23.34°$ $b=125.3cm$ Solving for a we get: $a=\frac{b}{tanB}$ $a=\frac{125.3cm}{tan(23.34°)}$ $a=\frac{125.3cm}{0.4315}$ $a=290.4cm$ To find side c (the hypotenuse), we can use the trigonometric ratio for sine. $sinB=\frac{b}{c}$ Where $B=23.34°$ $b=125.3cm$ Solving for c we get: $c=\frac{b}{sinB}$ $c=\frac{125.3cm}{sin(23.34°)}$ $c=\frac{125.3cm}{0.3962}$ $c=316.3cm$
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