Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.2 - The Law of Cosines - Exercise Set - Page 730: 33

Answer

$A\approx51^\circ, B\approx61^\circ, C\approx68^\circ$

Work Step by Step

Step 1. With the given numbers, we have $a=BC=4+3.5=7.5, b=AC=5+3.5=8.5,c=AB=5+4=9$ Step 2. Using the Law of Cosines, we have $c^2=a^2+b^2-2ab\ cosC$ or $9^2=7.5^2+8.5^2-2(7.5)(8.5)\ cosC$ which gives $cosC=0.3725$ and $C=acos(0.3725)\approx68^\circ$ Step 3. Using the Law of Sines, we have $\frac{sinA}{a}=\frac{sinC}{c}$ and $sinA=\frac{7.5sin(68^\circ)}{9}\approx0.7727$, thus $A=asin(0.7727)\approx51^\circ$ and $B\approx180^\circ-68^\circ-51^\circ=61^\circ$ Step 4. The solutions are $A\approx51^\circ, B\approx61^\circ, C\approx68^\circ$
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