SOLUTION: An airplane flies 180 miles from point X at a bearing of 125 degrees, and then turns and flies at a bearing of 230 degrees for 100 miles. How far is the plane from point X?

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Question 269111: An airplane flies 180 miles from point X at a bearing of 125 degrees, and then turns and flies at a bearing of 230 degrees for 100 miles. How far is the plane from point X?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!


     

We want to calculate the length of the green line D.

We will have two sides and the included angle if we can figure
out what the angle indicated by the red arc is.

The bottom part of the 125° angle below the horizontal is 
125°-90° or 35°.  By alternate interior angles it is
equal to the top part of the angle indicated by the red arc,
which is above the horizontal. And we can calculate the
bottom part of that angle by subtracting 270°-230°=40°.

So the angle indicated by the red arc is 35°+40° or 75°.

Now we can use the law of cosines to find the length of the
green line D.









or 190 miles to the nearest 10 miles, as the other two distances
seem to be rounded to, or 191 to the nearest mile.  How you round
the answer depends on what your teacher tells you.

Edwin
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