Question

Two ships sail from port P. One sails 14km due south while the other sails 17km on a bearing of 120 degrees. Calculate to one decimal place the distance between the ships.

Answer 1

I will assume that by a bearing of 120 degrees you mean
S 60° W , so we have a simple application of the cosine law:

From your sketch
x^2 = 14^2 + 17^2 - 2(14)(17) cos 60°

etc

Answer 2

Look at this like a triangle. Port P is the top point of the triangle. One sails 14km straight down (south) the other sails at an angle for 17km(this would be the hypotonus)
Remembering A squared + B squared = C squared
(14*14) + (B*B) =17 *17
196 + (B*B) = 289
B*B = 289-196
B*B = 93
B= square root of 93
B =9.643...….