Finding the distance between two points
A surveyor on one side of a river wishes to find the distance between points A and B on the opposite side of the river. On her side she chooses points C and Dwhich are 20m apart and measure the angles shown in the figure. Find the distance between A and B.
**credit given to those who show work only!
Homework Answers
find the angle CAD = 180 - 40 - 20 - 45 = 75 degree
AD / sin ACD = CD / sin CAD
AD = CD sin ACD / sin CAD
= 20 sin(50+45) / sin(75)
= 20.627
find the angle CBD = 180 - 20 - 50 -45 = 65 degree
BD/ sin BCD = CD/ sin CBD
BD = CD sin BCD / sin CBD
= 20 sin 20 / sin 65
= 21.984
use cosine rule to find AB
AB2 = AD2 + BD2 - 2(AD)(BD)cos(ADB)
= ( 20.627)2 + (21.984)2 - 2(20.627)(21.984)cos(50)
= 325.807
AB = √325.807
= 18.05 m
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