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July 27th, 2013, 05:49 AM   #1
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Courses in Trigonometry Question

Hi. This is the question:
A jet flew 140 mi on a course of 196 degrees and then 120 mi on a course of 106 degrees then the jet return to its starting point via the shortest route possible. Find the total distance that the jet traveled.

I found the answer for this. It's this one:
http://ph.answers.yahoo.com/question/in ... 233AAVgQcy

Now I understand everything else, but my problem is why they used the given angles to confirm that it is a right triangle. I know this has something to do with theorems on parallel lines, but I just can't picture how. I will need an illustration to understand this. Thank you.
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July 28th, 2013, 05:58 AM   #2
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[attachment=0:9h248etf]Flightpath.GIF[/attachment:9h248etf]
Path-length = 140 + 120 + ?34000 (by Pythagoras)
                  = 260 + 184.39 approximately
                  = 444.4 approximately.

The above is for any consistent choice of units, so you should add "Mi" throughout in your answer. The direction bearings given in the question are measured clockwise from the "bottom to top" direction in the above diagram, so you should be able to see why the angle shown as a right angle is exactly a right angle. Note that the answer you linked to is numerically slightly inaccurate.
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