A ship sails from a port,P, on a course of 060 degrees for 15km to a buoy ,Q. It then changes course in a direction 120 degrees from Q for 25 km to a rig R.

D = 15km @ 60deg + 25km @ 120deg.

X = hor. = 15cos60 + 25cos120 = -5km.
Y = ver. = 15sin60 + 25in120 = 34.64km.

tanA = Y/X = 34.64 / -5 = -6.9282,
A = -81.8 Deg., CW.
A = -81.8 + 180 = 98.2 Deg., CCW.

D = -5 / cos98.2 = 35km @ 98.2 Deg.,CCW

To determine the final position of the ship at rig R, we need to calculate the displacement of each leg of the journey.

First, let's calculate the displacement from the port P to the buoy Q. The ship sails on a course of 060 degrees for a distance of 15 km. To calculate the displacement, we can use trigonometry.

The displacement (D1) in the East direction can be determined using the cosine of the angle and multiplying it by the distance:

D1 = 15 km * cos(60 degrees)

Next, the displacement (D2) in the North direction can be determined using the sine of the angle and multiplying it by the distance:

D2 = 15 km * sin(60 degrees)

Now let's calculate the displacement from the buoy Q to the rig R. The ship changes course in a direction 120 degrees from Q for a distance of 25 km.

Again, we can use trigonometry to calculate the displacement. The displacement (D3) in the East direction can be determined using the cosine of the angle and multiplying it by the distance:

D3 = 25 km * cos(120 degrees)

Similarly, the displacement (D4) in the North direction can be determined using the sine of the angle and multiplying it by the distance:

D4 = 25 km * sin(120 degrees)

To find the final position at rig R, we need to sum up the displacements in the East and North directions:

East displacement (E) = D1 + D3
North displacement (N) = D2 + D4

So, the final position can be determined by combining the displacements:

Final position at rig R = (E, N)

Now, you can calculate the values using a scientific calculator or trigonometric tables to get the exact displacements and find the final position of the ship at rig R.