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 - Page 754: 24

Answer

$$C = {91.9^ \circ },\,\,\,\,AB = 847{\text{ft}},\,\,\,\,BC = 489.7{\text{ft}}$$

Work Step by Step

$$\eqalign{ & A = {35.3^ \circ },\,\,\,B = {52.8^ \circ }{\text{,}}\,\,\,AC = 675{\text{ft}} \cr & {\text{The side }}AC{\text{ is }}b = 675{\text{ft}} \cr & \cr & {\text{Find }}C \cr & C = {180^ \circ } - A - B \cr & C = {180^ \circ } - {35.3^ \circ } - {52.8^ \circ } \cr & C = {91.9^ \circ } \cr & \cr & {\text{Use the law of sines to find side }}a{\text{ or }}BC \cr & \frac{a}{{\sin A}} = \frac{b}{{\sin B}} \cr & a = \frac{{b\sin A}}{{\sin B}} \cr & a = \frac{{675\sin \left( {{{35.3}^ \circ }} \right)}}{{\sin \left( {{{52.8}^ \circ }} \right)}} \cr & {\text{Use a calculator}} \cr & a = 489.7{\text{ft}} \cr & BC = 489.7{\text{ft}} \cr & \cr & {\text{Use the law of sines to find side }}c{\text{ or }}AB \cr & \frac{c}{{\sin C}} = \frac{b}{{\sin B}} \cr & c = \frac{{b\sin C}}{{\sin B}} \cr & c = \frac{{675\sin \left( {{{91.9}^ \circ }} \right)}}{{\sin \left( {{{52.8}^ \circ }} \right)}} \cr & {\text{Use a calculator}} \cr & c = 847{\text{ft}} \cr & AB = 847{\text{ft}} \cr & \cr & {\text{Answer}} \cr & C = {91.9^ \circ },\,\,\,\,AB = 847{\text{ft}},\,\,\,\,BC = 489.7{\text{ft}} \cr} $$
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