Algebra 2 (1st Edition)

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

Chapter 13, Trigonometric Ratios and Functions - 13.2 Define General Angles and Use Radian Measure - 13.2 Exercises - Quiz for Lessons 13.1 and 13.2 - Page 865: 4

Answer

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Work Step by Step

Given: $B=42$ degrees $c=16$ Thus, $C=90$ It is a right triangle. Hence, the sum of two non-right angles of a triangle is 90 degrees: $A=90-B=90-42=48$ degrees We know $\cos B=\frac{a}{c}\\ \rightarrow a=c\cos B=18\times \cos 42\approx 13.38$ Apply the Pythagorean theorem to find c: $a^2+b^2=c^2\\b=\sqrt c^2-a^2\\c=\sqrt 16^2+(18\cos 42)^2\approx12.04$
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