Question 488945: Please help me solve this question: Villages A,B,C and D are such that B is 4km due east of A, C is 3km due south of B and D is 4km South50degreeWest from C. Calculate the distance and bearing of A from D.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Please help me solve this question: Villages A,B,C and D are such that B is 4km due east of A, C is 3km due south of B and D is 4km South50degreeWest from C. Calculate the distance and bearing of A from D.
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For you to understand my solution, we must work from the same diagram, so let us try to draw one:
Starting from point A, draw a 4 km horizontal line to B. (B is due East of A)
From B, draw a 3 km vertical down to C. (C is due South of B)
From C, draw a 4 km line rotated 50º clockwise from vertical to D. (D is 50º west of south from C)
Draw a line from D back to A.
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This is the basic diagram, but we need to construct additional lines and points:
From D, draw a vertical line up until is intersects with line AB. Call this point E.
Also from D, draw horizontal line (right) that intersects with a vertical line drawn from C. Call this point F.
Also from D, draw horizontal line(left) that intersects with a vertical line drawn from A. Call this point G.
We now should have a rectangle with the four corners labeled ABFG.
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DF/4=sin 50º
DF=4Sin50º=3.06
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CF/4=Cos 50º
CF=4cos50º=2.57
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AE=4-DF=4-3.06=.94
ED=3+CF=3+2.57=5.57
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Bearing angle=angle ADE; call this angle x
tan x=AE/ED=.94/5.57=.1688
arctan(.1688)=9.58º
x=9.58º
AD=AE/sinx=.94/sin 9.58º=5.64 km
Ans:
Bearing of A from D is 5.64 km N9.58ºW
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I hope this came out ok.
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