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: 18


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Work Step by Step

We are given $a, c, b$. Use law of cosines to find $c$: $$a^2=b^2+c^2-2bc\cos A\\ B=\arccos\frac{b^2+c^2-a^2}{2bc}\\b=\arccos\frac{20^2+23^2-24^2}{2(23)(20)} \approx 67.4$$ Use law of sines to find: $\frac{\sin B}{b}=\frac{\sin A}{a}\\\sin A=\frac{\sin B}{b}\times a\\\arcsin (\sin A)=\arcsin (\frac{\sin B}{b}a)\\A=\arcsin(\frac{\sin B}{b}. a)\\A\approx 62.2^\circ$ Since the sum of the triangle is $180^\circ$, we obtain: $$A+B+C=180^\circ\\C=180^\circ-A-B\\C=180^\circ -62.2^\circ -67.4^\circ\\C=50.4^\circ$$
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