A robot turtle is programmed using bearings to follow a path. He heats 5 m at a bearing of 110 degrees, then 8 m at a bearing of 210 degrees then 9 m at a bearing of 260 degrees.
How far is the turtle from its starting point and what bearing will retrun the turtle to its starting position?

This is what is called a traverse in surveying. The bearings can be thought of as azimuths

turning clockwise from due north(y-axis).

The first point is 110 degrees and ad distance of 5 meters. We find these distances and add

them to our starting point we can call (0,0) at the origin.

5cos(110)=-1.71
5sin(110)=4.7

The coordinates of the first point is (4.7,-1.71)

Now, do the other and add them to the last point coordinates.

8sin(210)+5cos(20)=0.70
8cos(210)+(-5sin(20))=-8.64

Continue until you get to the end.

If you do the rest correctly, you will get an angle of 38.67 degrees and a distance of

13.07 meters back to the starting point from the last point.