Elementary Technical Mathematics

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

Chapter 13 - Section 13.4 - Solving Right Triangles - Exercise - Page 460: 14

Answer

$A=60.14^{\circ}$. $c=83.74\;m$. $b=41.69\;m$.

Work Step by Step

The given values are $B=29.86^{\circ}$ $a=72.62\;m$. In a right angle triangle sum of other two angles is $90^{\circ}$. $A+B=90^{\circ}$ Isolate $A$. $A=90^{\circ}-B$ Plug value of $B$. $A=90^{\circ}-29.86^{\circ}$ Simplify. $A=60.14^{\circ}$. By using trigonometric ratios. $\frac{a}{c}=\cos{B}$ Isolate $c$. $c=\frac{a}{\cos{B}}$ Plug all values. $c=\frac{72.62\;m}{\cos{(29.86^{\circ})}}$ By using degree calculator simplify. $c=83.74\;m$ (rounded value). By using trigonometric ratios. $\frac{b}{a}=\tan{B}$ Isolate $b$. $b=a\cdot \tan{B}$ Plug all values. $b=(72.62\;m)\cdot \tan{(29.86^{\circ})}$ By using degree calculator simplify. $b=41.69\;m$ (rounded value).
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