A ship is 180 kilometres away from a port P on a bearing of 63 degrees. Another ship is 245 kilometres away from port P on a bearing of 146 degrees. Calculate the distance between the two ships.

While this problem could be done simply by inputting the appropriate numbers into the correct formula, it is good practice to draw a diagram of the problem in order to minimise any silly mistakes that may be made. Upon drawing the diagram you should be able to see that the placement of the two ships(which we can call A and B) and the port make a triangle and that the information you are given enables you to use the cosine rule to calculate the distance between the two ships.
We can calculate the angle between ship A and ship B is (146-63), since the bearing of ship B is taken from port. The distance between the two ships can be assigned to the variable c.The values are substituted into the cosine rule to result in : c^2 = (180^2) + (245^2) -(2180245*cosC)This is simplified to: c^2 = 81676.12Therefore c = 285.8 kilometres.