Question 1189698
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Let's say the surveyor is at point A. 
He measures an angle of 56 degrees at this location when looking at the other corners B and C. 
So angle A = 56.


The side opposite angle A is side 'a'
b is opposite angle B
c is opposite angle C


The surveyor figured out that a = 60 meters and b = 70 meters. Assume side b is to the left of point A.


We have these properties
angle A = 56 degrees
side a = 60 meters
side b = 70 meters


Let's use the law of sines to see if we can figure out angle B
sin(A)/a = sin(B)/b
sin(56)/60 = sin(B)/70
sin(B) = 70*sin(56)/60
sin(B) = 0.9672105 approximately
B = arcsin(0.9672105) or B = 180-arcsin(0.9672105)
B = 75.287079 or B = 180-75.287079
B = 75.287079 or B = 104.712921


If B = 75.287079, then,
C = 180-A-B
C = 180-56-75.287079
C = 48.712921
which forms a valid triangle.


If B = 104.712921, then
C = 180-A-B
C = 180-56-104.712921
C = 19.287079
which forms a different triangle


So the info that the surveyor currently has is <u>not</u> enough information. 
Two triangles are possible, which means the surveyor needs to go back and do at least one more measurement.


The client should <u>not</u> pay the surveyor (at least not until the surveyor completes the task). 


For more information, search out "SSA ambiguous case" or "law of sines ambiguous case".
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