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