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: 68

Answer

$$A \approx 228.25{\text{y}}{{\text{d}}^2}$$

Work Step by Step

$$\eqalign{ & a = 25.4{\text{yd}},\,\,\,b = 38.2{\text{yd,}}\,\,\,c = 19.8{\text{yd}} \cr & {\text{First}},{\text{ find the semiperimeter }}s \cr & s = \frac{1}{2}\left( {a + b + c} \right) \cr & s = \frac{1}{2}\left( {25.4 + 38.2 + 19.8} \right) \cr & s = 41.7 \cr & \cr & {\text{Now use Heron's formula to find the area }}A \cr & A = \sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)} \cr & A = \sqrt {41.7\left( {41.7 - 25.4} \right)\left( {41.7 - 38.2} \right)\left( {41.7 - 19.8} \right)} \cr & {\text{Use a calculator}} \cr & A \approx 228.25{\text{y}}{{\text{d}}^2} \cr} $$
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