Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have a trigonometry problem that I can't figure out. It goes like this:

Points M and P are the same distance from a third point, O. The bearing of M from O is o38 degrees and the bearing of P from O is 152 degrees. I know the bearings add up to 190 and the answer to the multiple choice question is D: between 180 and 270, but what I can't figure out is how to get the bearing from P to M. Can anyone help?

share|cite|improve this question
up vote 1 down vote accepted

I think "the bearing of M from O is $38$ degrees" means if you draw a ray due East from O and put a point Q on it then you have to rotate the segment OQ $38$ degrees counterclockwise to get it to lie along the segment OM. And I think the question of the bearing from P to M is, through what angle must we rotate a segment extending due East from P to get it to lie along the segment from P to M.

If I have all that wrong, then ignore what follows.

Draw a diagram with all these points and lines. Angle POM is $152-38=114$ degrees. Triangle POM is isosceles, so angle PMO is $33$ degrees. Let the line due East from P cross OM at W. Angle PWO equals angle WOX (vertical angles), so it's $38$ degrees. So angle PWM is $142$ degrees. That makes angle MPW $5$ degrees, and that's the bearing of M from P.

share|cite|improve this answer
Thank you so much! You are a great help! – user61474 Feb 8 '13 at 12:16
If you find it serves your purposes, you can "accept" it by clicking in the little check mark next to it. – Gerry Myerson Feb 8 '13 at 12:32
Seems good, except I remember bearing to refer to clockwise angle from due north (or direction of motion if you are in a ship). However whether you take East or North, counterclockwise or clockwise as your convention, the construction is similar and I think the angle in the new reference would be also same... – Macavity Feb 8 '13 at 13:00

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.