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 893: 36

Answer

See below

Work Step by Step

Since the sum of the triangle is $180^\circ$, we obtain: $$A+B+C=180^\circ\\C=180^\circ-A-B\\C=180^\circ -72^\circ -44^\circ\\C=64^\circ$$ Use law of sines to find: $$\frac{a}{\sin A}=\frac{b}{\sin B}\\ a=\frac{b}{\sin B}\times \sin A\\A=\arcsin(\frac{\sin B}{b}. a)\\A\approx 19.17^\circ$$ $$\frac{c}{\sin C}=\frac{b}{\sin B}\\c=\frac{b}{\sin B}\times \sin C\\c\approx18.11^\circ$$
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