A plane flies 1.3 hrs at 110 mph on a bearing of 38 degrees. It then turns and flies 1.5 hrs at the same speed on a bearing of 128 degrees. How far is the plane from its starting point?

Question

radar · Answer

Bearings are based on True North which is a bearing of 0 degrees, then Clockwise with due East being 90 degrees etc.

If you will sketch those set of bearing, the plane made a change of heading of 90 degrees and ended up flying in a Southeastern direction.  From your sketch you should note that he made a turn of 90 degrees.  Use Pythagorean.

radar · Answer

The distance will be the hypotenuse of a right triangle whose legs are the two distances traveled.  Compute those distances and solve for the hypotenuse.

anonymous · Answer

I get 218.34 mi but answer key says 220 mi. not sure where I'm going wrong.

radar · Answer

Let work iot.  the 38 degree leg was 1.3 X 110 or 143 miles
the 128 degree leg was 1.5 X 110 or 165 miles
143^2 + 165^2 = 47674
sqrt47674 = 218.34
I got the same as you.  I think that is correct, the answer has been rounded off.

radar · Answer

Is it a multiple choice question?

anonymous · Answer

thank you. i have been racking my brain trying to figure out how i was off.  no its not multiple choice.  i work the problem then check the back to make sure I'm right.

radar · Answer

Well bearing change from 38 to 128 degree is a 90 degree change.  Oh well speeds are usually given in knots, maybe there was some info missing.  But I feel you have done it correctly.

radar · Answer

Good luck with these problems.

anonymous · Answer

thanks

anonymous · Answer

Refer to the attached Mathematica solution, a more general approach.

radar · Answer

Well it agrees.  thanks robtobey.

anonymous · Answer

@radar 
Thank you for the medal.
Used the vector method because it will solve any combination of headings.
Vectors can get messy working with only pencil and paper.