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# "Bearing" question - finding distance between two objects watch

1. Dear friends,

I am having problem solving the following question related to "bearing" in trigonometry.

A motorboat is 10 km South of a lighthouse and is on a course of 053 degrees. What is the shortest distance between the motorboat and the lighthouse?

My confusion is how does a boat travel 10 km South of a lighthouse and making an angle of 53 degrees clockwise from North. Is there something wrong with the question itself?

2. No it means the boat begins at a point 10km due south of the lighthouse, and then travels at a bearing of 053 degrees. What is the closest it gets to the lighthouse while travelling that path.
3. the question is correct. as the boat moves along its bearing, the line connecting the boat to the lighthouse shortens, reaches its minimum value, then lengthens once more.
4. 10sin53
5. It's a very poorly worded question unless there is other previous information missing from the OP's text (i.e. making it a vector calculation).

As it stands, the shortest distance to the lighthouse would be as stated: 10km due north.

If the question had asked for the closest distance to the lighthouse, it would take on a whole new context for the answer.
6. Thanks all of you for all the info and discussion that enabled me to arrive at the solution. Really helped me understanding and solving the question. Highly appreciate it.

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Updated: January 23, 2017
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