SOLUTION: I have have been struggling with this for half of the day. I would appreciate any assistance with the following problem: Two boats leave the port at the same time. The first boat

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Question 143649: I have have been struggling with this for half of the day. I would appreciate any assistance with the following problem:
Two boats leave the port at the same time. The first boat travels due east at 14 mph, and the second boat travels at 28 mph in the direction of N30 degrees E . To the nearest tenth of a mile, how far apart will the boats be in a half an hour? (Hint: 0.5 represents a half an hour.)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If I read it right, N30 degrees east means 30 degrees east of north.
In that case, first find out how far each boat goes in .5 hr.
boat going east: 14%2A+.5+=+7mi
boat going N30E: 28%2A.5+=+14mi
To proceed, you've got to know that a 30:60:90 triangle has sides
that are in the proportion 1:sqrt%283%29:2. Note that
the sides are opposite their respective angles. So, the boat that
travels 28 mi/hr is at an angle of 60 degrees with east. The
distance vectors are in the proportion 14%2F7+=+2%2F1 with 60
degrees between them. The distances must be in the proportion
1:sqrt%283%29:2, or in this case,
7:7%2Asqrt%283%29:14
So, the distance between them to the nearest tenth is
7%2Asqrt%283%29+=+12.1mi