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: 16

Answer

$A=35.5^{\circ}$. $B=54.5^{\circ}$. $b=3415.25\;ft$.

Work Step by Step

The given values are $a=2436\;ft$ $c=4195\;ft$. By using trigonometric ratios. $\frac{a}{c}=\sin{A}$ Isolate $A$. $A=\sin^{-1}\left(\frac{a}{c} \right )$ Plug all values. $A=\sin^{-1}\left(\frac{2436\;ft}{4195\;ft} \right )$ By using degree calculator simplify. $A=35.5^{\circ}$ (rounded value). In a right angle triangle sum of other two angles is $90^{\circ}$. $A+B=90^{\circ}$ Isolate $B$. $B=90^{\circ}-A$ Plug value of $A$. $B=90^{\circ}-35.5^{\circ}$ Simplify. $B=54.5^{\circ}$. By using Pythagorean theorem. $b=\sqrt{c^2-a^2}$ Plug all values. $b=\sqrt{(4195\;ft)^2-(2436\;ft)^2}$ Simplify. $b=\sqrt{17598025\;ft^2-5934096\;ft^2}$ $b=\sqrt{(11663929\;ft^2)}$ $b=3415.25\;ft$.
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