Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 13, Trigonometric Ratios and Functions - 13.5 Apply the Law of Sines - 13.5 Exercises - Skill Practice - Page 886: 15

Answer

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Work Step by Step

The sum of the angles of the triangle is $180^\circ$ $$A+B+C=180^\circ\\B=180^\circ-B-C\\B=180^\circ-42^\circ-73^\circ\\B=65^\circ$$ Use the law of sines: $$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{y\sin C}$$ First we obtain: $\frac{a}{\sin A}=\frac{c}{y\sin C}\\a=\frac{c}{\sin C}\times\sin A=\frac{34}{\sin 73^\circ}\times\sin 42^\circ\approx 23.79$ Then $\frac{b}{\sin B}=\frac{c}{\sin C}\\b=\frac{c}{\sin C}\times\sin B=\frac{34}{\sin 73^\circ}\times\sin {65}^\circ\approx32.22$
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