Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 7 - Section 7.2 - The Law of Cosines - 7.2 Problem Set - Page 378: 26



Work Step by Step

$a=832ft,b=623ft,c=345ft$ For angle A, as per Laws of cosines, $a^{2}=b^{2}+c^{2}-2bc(cosA)$ $cosA=\frac{623^{2}+345^{2}-832^{2}}{2\times623\times345} = -0.431$ So, $A=115.5^{\circ}$ $b^{2}=c^{2}+a^{2}-2ca(cosB)$ $cosB=\frac{345^{2}+832^{2}-623^{2}}{2\times345\times832}=0.737$ $B=42.5^{\circ}$ Hence, $C=180^{\circ}-(A+B)=180^{\circ}-(115.5^{\circ}+42.5^{\circ})=180^{\circ}-158^{\circ}=22^{\circ}$ So, $A=115.5^{\circ},B=42.5^{\circ},C=22^{\circ}$
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