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 730: 15


$b\approx5.4, A\approx68^\circ, C\approx22^\circ$

Work Step by Step

Step 1. Based on the given conditions, using the Pythagorean Theorem, we have $b=\sqrt {a^2+c^2}=\sqrt {5^2+2^2}=\sqrt {29}\approx5.4$ Step 2. For angle $A$, in the right triangle, we have $tanA=\frac{a}{c}=2.5$, thus $A=tan^{-1}(2.5)\approx68^\circ$ Step 3. We can find the angle as $C=90^\circ-68^\circ=22^\circ$ Step 4. We solved the triangle with $b\approx5.4, A\approx68^\circ, C\approx22^\circ$
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