Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 13, Trigonometric Ratios and Functions - 13.6 Apply the Law of Cosines - 13.6 Exercises - Skill Practice - Page 892: 29



Work Step by Step

By Heron's Formula, we know: $$A=\sqrt{s(s-a)(s-b)(s-c)}$$ Where: $$s=\frac{a+b+c}{2}$$ Thus, we find: $$s=\frac{81+67+71}{2}=\frac{219}{2} \\ A=\sqrt{\frac{219}{2}\left(\frac{219}{2}-81\right)\left(\frac{219}{2}-67\right)\left(\frac{219}{2}-71\right)} \\ A=\frac{3\sqrt{9077915}}{4}$$
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