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    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?


    Thanks in advance.
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    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.
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    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.
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    10sin53
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    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.
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    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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