Questions: Two ships leave a harbor at the same time. One ship travels on a bearing S 14° W at 13 miles per hour. The other ship travels on a bearing N 75° E at 12 miles per hour. How far apart will the ships be after 2 hours? The distance is approximately □ miles. (Round to the nearest tenth as needed.)

Two ships leave a harbor at the same time. One ship travels on a bearing S 14° W at 13 miles per hour. The other ship travels on a bearing N 75° E at 12 miles per hour. How far apart will the ships be after 2 hours?

The distance is approximately □ miles. (Round to the nearest tenth as needed.)

Transcript text: Two ships leave a harbor at the same time. One ship travels on a bearing $\mathrm{S} 14^{\circ} \mathrm{W}$ at 13 miles per hour. The other ship travels on a bearing $N 75^{\circ} \mathrm{E}$ at 12 miles per hour. How far apart will the ships be after 2 hours? The distance is approximately $\square$ miles. (Round to the nearest tenth as needed.)

Solution

Solution Steps

Step 1: Convert Bearings to Cartesian Coordinates

Step 2: Calculate the Distance

The distance between the two ships is calculated using the distance formula, resulting in $\sqrt{(6.212 + 25.228)^2 + (23.182 + 6.290)^2} = 43.1$ miles.