Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 7 - Review Exercises - Page 350: 26


The length of the brace is 10.6 feet

Work Step by Step

Let angle $B = 115^{\circ}$ Let angle $C = 22^{\circ}$ Let angle $A$ be the angle of the triangle between the brace and the wall. We can find angle $A$: $A+B+C = 180^{\circ}$ $A = 180^{\circ}-B-C$ $A = 180^{\circ}-115^{\circ}-22^{\circ}$ $A = 43^{\circ}$ We can use the law of sines to find the length of the brace $b$: $\frac{b}{sin~B} = \frac{8.0~ft}{sin~A}$ $b = \frac{8.0~ft~sin~B}{sin~A}$ $b = \frac{(8.0~ft)~sin~(115^{\circ})}{sin~43^{\circ}}$ $b = 10.6~ft$ The length of the brace is 10.6 feet
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