# Field Exercise

worked example:

consider three objects A B and C on a field.
A and B are a known 25.00m apart.
Using a protractor C is found to be 87.63degrees from the line AB "length c" measured at B and 77.12degrees measured from A.
Knowing that the total of the angles in a triangle add to 180 degrees, it can be inferred that:
angle C is 180-(A+B)
=180-(77.12+86.73)
=180-163.85=16.15.
Using the sine law:
a/sinA=b/sinB=c/sinC, we can work out the lengths AC (or b) and BC (or a)
b=(c/sinC) x sinB
sinB = sin(86.73)=0.9983718
sinC = sin(16.15)=0.2781530
thus b=(25/0.2781530)x0.9983718=89.87859x0.9983718= 89.73m
Note the discrepancy between image and calulated due to rounding errors!
It is also possible to estimate the distance from the line AB as this would form a right angled triangle.
Using B again the Hypotenuse is (our calculation) 89.73m and the angle is 86.73 degrees. The adjacent is 89.73x sin(77.12)=87.47m

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