January 15th, 2016, 10:47 AM  #1 
Senior Member Joined: Jan 2015 From: London Posts: 108 Thanks: 2  Bearings? Help
If a habour H is 25km due North of an airport A. Town T is 50km due East of H. So what is the bearing of T from A? I'm having trouble with working it out. Please help. Last edited by skipjack; January 15th, 2016 at 03:00 PM. 
January 15th, 2016, 01:59 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,641 Thanks: 625 
Let a be the angle of interest. a=arctan(2). a is the angle counterclockwise from due north.

January 15th, 2016, 02:08 PM  #3 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 
The first thing to do is make a sketch. I'm assuming you've already done that. Now, note that $\triangle AHT$ is a right triangle with $\angle H$ as the right angle. We want to find $\theta = \angle HTA$. We find $\tan \theta = \dfrac{HA}{HT} = \dfrac{25}{50} = \dfrac{1}{2}$ And thus $\theta = \tan^{1}\left(\dfrac{1}{2}\right)\approx26.57^\circ$ Now you just have to write it as a bearing. 
January 15th, 2016, 02:18 PM  #4 
Senior Member Joined: Jan 2015 From: London Posts: 108 Thanks: 2 
The answer is 63.4, but can I have the working?
Last edited by skipjack; January 15th, 2016 at 03:03 PM. 
January 15th, 2016, 02:29 PM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,885 Thanks: 1088 Math Focus: Elementary mathematics and beyond 
The bearing of T from A is $\displaystyle (\tan^{1}(2))^\circ$ due east from north. As previously suggested, make a diagram.

January 15th, 2016, 03:06 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 19,968 Thanks: 1850 
The answer is 63.4 degrees to 3 significant figures (because tan of the bearing is 2).

January 15th, 2016, 03:16 PM  #7 
Math Team Joined: Jul 2011 From: Texas Posts: 2,780 Thanks: 1431 
Didn't someone say, "make a sketch" ? ... makes the whole problem rather elementary if you paid heed to their good advice.

January 16th, 2016, 06:14 AM  #8 
Senior Member Joined: Jan 2015 From: London Posts: 108 Thanks: 2 
So what would be the bearing from A to T? I think it would be 243 but I don't know how to work it out? Last edited by skipjack; January 16th, 2016 at 06:42 AM. 
January 16th, 2016, 06:40 AM  #9 
Global Moderator Joined: Dec 2006 Posts: 19,968 Thanks: 1850 
Stick with 63.4 degrees. There's no need to add on a further 180 unless you want the bearing of A from T, which isn't what you asked for originally.

January 16th, 2016, 06:57 AM  #10 
Senior Member Joined: Jan 2015 From: London Posts: 108 Thanks: 2 
I know but i was curious of what A to T was so how would I work that out?


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