Two ships leave a harbor at the same time. One ship travels on a bearing S13°W at 15 miles per hour. The other ship travels on a bearing N75°E at 9 miles per hour. How far apart will the ships be after 3 hours?
To solve this problem, we can use the Law of Cosines to find the distance between the two ships after 3 hours.
First, let's find the distance each ship has traveled after 3 hours. Ship 1 has traveled 15 mph * 3 hours = 45 miles. Ship 2 has traveled 9 mph * 3 hours = 27 miles.
Next, we can use trigonometry to determine the angle between the two ships' paths. The sum of the two bearings is S13°W + N75°E = 90°. Therefore, the angle between the two ships' paths is 180° - 90° = 90°.
Now, we can use the Law of Cosines to find the distance between the two ships after 3 hours:
d^2 = 45^2 + 24^2 - 2 * 45 * 24 * cos(90°)
d^2 = 2025 + 729 - 2 * 45 * 27 * 0
d^2 = 2754
d = √2754
d ≈ 52.5 miles
Therefore, the two ships will be approximately 52.5 miles apart after 3 hours.