trigonometry
posted by John .
A ship at A is to sail to C, 56km north and 258km east of A. After sailing N25°10’E for 120mi to P, the ship is headed toward C. Find the distance of P from C and the required course to mean C.

duplicate question.
Call the vector from B to C "v2"
Call the vector from the starting point to C "v3".
v3 = 56 j + 258 i
Call the first leg of the voyage, from A to B, "v1"
Perform the vector operation
v2 = v3  v1
The magnitude and direction of v2 will be your answer.