Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 8 - Application of Trigonometry - 8.2 The Law of Cosines - 8.2 Exercises - Page 771: 69

Answer

$$A \approx 3650{\text{f}}{{\text{t}}^2}$$

Work Step by Step

$$\eqalign{ & a = 76.3{\text{ft}},\,\,\,b = 109{\text{ft,}}\,\,\,c = 98.8{\text{ft}} \cr & {\text{First}},{\text{ find the semiperimeter }}s \cr & s = \frac{1}{2}\left( {a + b + c} \right) \cr & s = \frac{1}{2}\left( {76.3 + 109 + 98.8} \right) \cr & s = 142.05 \cr & \cr & {\text{Now use Heron's formula to find the area }}A \cr & A = \sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)} \cr & A = \sqrt {142.05\left( {142.05 - 76.3} \right)\left( {142.05 - 109} \right)\left( {142.05 - 98.8} \right)} \cr & {\text{Use a calculator}} \cr & A \approx 3650{\text{f}}{{\text{t}}^2} \cr} $$
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