Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 8 - 8.2 - Law of Cosines - 8.2 Exercises - Page 574: 37


$Area=\frac{\sqrt {8855}}{4}\approx23.53$

Work Step by Step

$s=\frac{a+b+c}{2}=\frac{6+12+17}{2}=\frac{35}{2}$ $Area=\sqrt {s(s-a)(s-b)(s-c)}=\sqrt {\frac{35}{2}(\frac{35}{2}-6)(\frac{35}{2}-12)(\frac{35}{2}-17)}=\sqrt {\frac{35}{2}(\frac{35}{2}-\frac{12}{2})(\frac{35}{2}-\frac{24}{2})(\frac{35}{2}-\frac{34}{2})}=\sqrt {\frac{35}{2}\frac{23}{2}\frac{11}{2}\frac{1}{2}}=\sqrt {\frac{8855}{16}}=\frac{\sqrt {8855}}{4}\approx23.53$
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