A farmer wants to fence off his four-sided plot of flat land. He measures the first three sides, shown as A, B, and C in the figure, and then correctly calculates the length and orientation of the fourth side D. What is his result?
Consider the following figure:
The east distance is the component in the horizontal direction.
The north distance is the vertical component
Based from the figure, we can easily see that the order is reversible in the addition of vectors. We say that
Consider the right triangle formed by the legs A, B, and R. We know that A is 18 m, B is 25 m, and we are solving for the magnitude of R. We can do this by using the Pythagorean Theorem. That is
So, the distance is about 30.8 meters from the starting point. To solve for the value of the unknown angle, φ, we can use the tangent function. That is
Therefore, the compass angle is