Two ships leave a harbor at the same time. one ship travels on a bearing upper s 12 degrees upper w at 18 miles per hour. the other ship travels on a bearing upper n 75 degrees upper e at 12 miles per hour. how far apart will the ships be after 2 hours?

Between N75E and E there are (90-75)=15°
Between E and S there are 90°
Between South and S12°W there 12°
Applying cosine rule 
Another way is to measure all angles clockwise from north (called azimuth) The ship at S12°W is at 180+12 = 192° 
The ship at N75°E is at 75° 
Angle between them is 192-75 = 117°

Applying cosine rule:
c=√(36²+24²-2×36×24cos117)
c=√2656.496
c=51.54 mi