Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 8 - Application of Trigonometry - 8.1 The Law of Sines - 8.1 Exercises: 17

Answer

$BC=\dfrac {76\times \sin \angle A}{\sin \angle C}=\dfrac {76\times \sin 27.2}{\sin 115.5}\approx 38.49;$ $AC=\dfrac {76\times \sin \angle B}{\sin \angle C}=\dfrac {76\times \sin 37.3}{\sin 115.5}\approx 51.03$

Work Step by Step

$\dfrac {76}{\sin \angle C}=\dfrac {BC}{\sin \angle A}=\dfrac {AC}{\sin \angle B};\angle B=180-\angle A-\angle C=180-27.2-115.5=37.3\Rightarrow $ $BC=\dfrac {76\times \sin \angle A}{\sin \angle C}=\dfrac {76\times \sin 27.2}{\sin 115.5}\approx 38.49;AC=\dfrac {76\times \sin \angle B}{\sin \angle C}=\dfrac {76\times \sin 37.3}{\sin 115.5}\approx 51.03$
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