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: 36


$A\approx41^\circ, B\approx71^\circ, C\approx68^\circ$

Work Step by Step

Step 1. Using the distance formula with the given numbers, we have $a=BC=\sqrt {(4-1)^2+(5-3)^2}\approx3.6$, $b=AC=\sqrt {(1)^2+(-5)^2}\approx5.1$, $c=AB=\sqrt {4)^2+(-3)^2}=5$ Step 2. Using the Law of Cosines, we have $b^2=a^2+c^2-abc\ cosB$ or $5.1^2=3.6^2+5^2-2(3.6)(5)cosB$ which gives $cosB\approx0.3319$ and $B=acos(0.3319)\approx71^\circ$ Step 3. Using the Law of Sines, we have $\frac{sinC}{c}=\frac{sinB}{b}$ and $sinC=\frac{5sin(71^\circ)}{5.1}\approx0.9270$ thus $C=asin(0.9270)\approx68^\circ$ and $A\approx180^\circ-71^\circ-68^\circ=41^\circ$ Step 4. The solutions are $A\approx41^\circ, B\approx71^\circ, C\approx68^\circ$
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