My Math Forum Bearings? Help

 Trigonometry Trigonometry Math Forum

 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: 6,416 Thanks: 557 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: 672 Thanks: 239 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: 7,692 Thanks: 976 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: 18,416 Thanks: 1462 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

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Didn't someone say, "make a sketch" ? ... makes the whole problem rather elementary if you paid heed to their good advice.
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 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: 18,416 Thanks: 1462 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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