Elementary Technical Mathematics

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

Chapter 16 - Cumulative Review - Page 568: 18


The measure of angle A is $44{}^\circ $

Work Step by Step

Here, $a=18.2cm,b=20.5cm$ and $c=26.1cm$ Use the law of cosines to find the measure of angle A as, ${{a}^{2}}={{b}^{2}}+{{c}^{2}}-2bc\text{ }\cos A$ …… (1) Substitute the values of a, b and c in equation (1), $\begin{align} & {{\left( 18.2 \right)}^{2}}={{\left( 20.5 \right)}^{2}}+{{\left( 26.1 \right)}^{2}}-2\left( 20.5 \right)\left( 26.1 \right)\text{ }\cos A \\ & 331.24=416.16+681.21-\left( 1070.1 \right)\text{ }\cos A \\ & 331.24=1097.37-\left( 1070.1 \right)\text{ }\cos A \end{align}$ Subtract 1097.37 from both sides: $\begin{align} & 331.24-1097.37=1097.37-\left( 1070.1 \right)\text{ }\cos A-1097.37 \\ & -766.13=-\left( 1070.1 \right)\text{ }\cos A \end{align}$ Divide both sides by $-1070.1$ to isolate $\cos A$, $\begin{align} & \frac{-766.13}{-1070.1}=\frac{-1070.1}{-1070.1}\text{ }\cos A \\ & 0.7159=\cos A \end{align}$ Therefore, the value of A is, $\begin{align} & A={{\cos }^{-1}}\left( 0.7159 \right) \\ & =44{}^\circ \end{align}$ Therefore, the measure of angle A is $44{}^\circ $.
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