Question 1189698: Hey, Can anyone help me with this question I am really confused. Thank you.
A surveyor is mapping a triangular field. From one corner he sights between the two opposite corners and finds an angle of 56°. He knows that he length of the opposite side of the field is 60m while the side to his left is 70m. The surveyor creates one drawing of the field and sends the single drawing and a bill to the client. Should the client pay the bill? Explain your reasoning
Found 4 solutions by Alan3354, ikleyn, greenestamps, math_tutor2020:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A surveyor is mapping a triangular field. From one corner he sights between the two opposite corners and finds an angle of 56°. He knows that he length of the opposite side of the field is 60m while the side to his left is 70m. The surveyor creates one drawing of the field and sends the single drawing and a bill to the client. Should the client pay the bill? Explain your reasoning
-------------------------
2 sides and an angle is sufficient to find the perimeter and the area of the triangle.
=============
Payment depends on the agreement between the 2 parties.
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
Honestly, as I read the post, I do not see any logical connection between the given part and the question . . .
May be, connection is illogical, but in this case it is out f Math.
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
Both of the other tutors missed the point of the problem.
Two sides and an angle is NOT enough to determine the triangle, if the known angle is not between the two known sides (the dreaded ASS or SSA case).
70*sin(56 degrees) is less than 60; that means with the given information there are two possible triangles.
That means the surveyor did not do his job properly; therefore, the client should not pay the bill.
Answer by math_tutor2020(3816)  (Show Source):
You can put this solution on YOUR website!
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 not enough information.
Two triangles are possible, which means the surveyor needs to go back and do at least one more measurement.
The client should not 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".
|
|
|
