Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.2 - The Law of Cosines - Exercise Set - Page 731: 47

Answer

$417.4\ ft$ and $398.2\ ft$
1585749089

Work Step by Step

Step 1. Draw a diagram as shown in the figure. Step 2. For the left triangle, we have the angle $B=90^\circ+7^\circ=97^\circ$ Step 3. Using the Law of Cosines, we have $b^2=(400)^2+(80)^2-2(400)(80)cos97^\circ\approx174,200$ Thus $b\approx417.4\ ft$ Step 4. For the right triangle, we have the angle $D=90^\circ-7^\circ=83^\circ$ Step 5. Using the Law of Cosines, we have $d^2=(400)^2+(80)^2-2(400)(80)cos83^\circ\approx158,600$ Thus $d\approx398.2\ ft$
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