Question

Two ships leave port at the same time. The first ship is sailing on a bearing of 037∘, the second ship is sailing on a bearing of 284∘.
The speed of the first ship is 14km h−1. The speed of the second ship is 9km h−1.

What is the distance between the two ships after three hours? Give your answer rounded to the nearest kilometre.

Answer 1

Answer:

58 km

Step-by-step explanation:

The first ship sails a distance of 42 km, the second one traveling 27 km.

The first ship's location can be found by multiplying the sine and cosine of its angle by its radius (42 km). 42cos(37 degrees) = 33.54 km north 42sin(37 degrees) = 25.28 km east. Doing the same for the second ship with its respective values gets us  26.20 km west and 6.53 km north. Solving the Pythagorean theorem with their combined horizontal distances (51.48 km, 27.01 km) gets us a final rounded distance of 58 km.