# 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**/sin**A**=**b**/sin**B**=**c**/sin**C**, we can work out the lengths **AC** (or **b**) and **BC** (or **a**)

**b**=(**c**/sin**C**) x sin**B**

sin**B** = sin(86.73)=0.9983718

sin**C** = 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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