how do i draw and calculate the bearing and distance of this question

Question

Peter, Sue and Alix are sea-kayaking. Peter is 430m from Sue on the bearing 113degres, Alix is on bearing 210degres and is 310m from Sue. Find the distance and the bearing of Peter from Alix.

Answer 1

This is hard to answer with words alone, so try to follow closely:

1) Draw an x-y coordinate set of axes with x being horizontal and y vertical. Label the origin where they cross as "S" for Sue's location.

2) With "0" degrees along the horizontal going to the right and 90 degrees being vertical straight up, draw a line that is 113 degrees from horizontal moving counter-clockwise(ccw). Label the length of the line as 430m and the endpoint "P" for Peter.

3) Draw another line that is 210 degrees ccw from horizontal. Label this length 310m and the endpoint "A" for Alix.

4) Draw a line from A to P. You now have a triangle with two side lengths given and the angle between the 2 as 210-113, which equals 107 degrees.

5) You can find the length between A and P by using the Law of Cosines and the bearing as the angle between the 310m and the length you just found by adding 30 degrees to it. That angle can be found by using the Law of Sines.

6) The answers I got are 599.121m and bearing 73.34 degrees.

Hope this helps!