Two ships leave a harbor at the same time.

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Sounds like a bar joke is about to begin, I have a question on an answer in my homework. I understand the concept of directions/angles. I for some reason stumped on this one question.

Here is the full question:

Two ships leave a harbor at the same time. One ship travels on a bearing S13°W at 10 miles per hour. The other ship travels on a bearing N75°E at 8 miles per hour. How far apart will the ships be after 22 ​hours?

I have made a half compass N and S poles. This isn't the prettiest thing in the world but this is kinda how I comprehended it, looks incredibly wrong(enjoy the galaxy paint):

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2 Answers

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From the above diagram $13^{\circ}$ is the angle travelled towards west and $75^{\circ}$ is the angle travelled towards East.

$220$ is the distance travelled towards west in $22$ hours.

$176$ is the distance travelled towards East in $22$ hours.

Now we need to find $x$ and you can use Law of Cosines.

$$x^2=(220)^2+(176)^2-2(220)(176)\cos(118^{\circ})$$Solve for $x$ and that will be your answer.

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1. Calculate the angle between their paths
2. Calculate the length of each path
3. Form a triangle and use the law of cosines for the unknown side (the distance between them)

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