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In general, you're right: you have to know three of the six sides or angles to solve a triangle.

If we look at this from the perspective of one of the lighthouse keepers, 
though, it looks different.  He can see the boat on the reciprocal bearing, 
and draw on his chart a line through his known position and the boat.

He can then call the keeper of the other lighthouse, get the bearing that 
fellow observes, and draw a line through that lighthouse and the boat.  He 
now knows where the boat is.

If you have the chart on the boat, you can do the same thing, and know exactly 
where you are.  There's no paradox here: the chart gives you the extra 
information you needed.

So, as the problem was stated, the answer you gave is certainly correct.  If 
you have a chart which correctly shows the positions of the lighthouses (and 
you've correctly identified them) you know your position.  Without the chart, 
if you only know the distance between lighthouses, you're still at sea.

Nels

----- Original Message -----
From: David Weilacher 
Date: Wednesday, March 3, 2004 9:44 am
Subject: Re: Question about navigating......

> Except for two special cases I think not.
>
> Those would be if you knew you formed a right angle from your boat
> to one tower then the other.
> ...or if you knew you were equi-distant from both of them.
>
>
>
> -----Original Message-----
> From: Rene Schmidt 
> Sent: Mar 3, 2004 10:18 AM
> To: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM
> Subject: Question about navigating......
>
> Good Morning,
>
> I am a new member to this list. Some sailing friends
> of mine have a little bet that I am hoping some
> super-navigator can help answer.
>
> We are sailing and see two lighthouses in the
> distance. The distance between the two are known (for
> example 2 kilometers). We have a compass and we can
> take a reading of the 2 lighthouses (for example 20
> degrees off of magnetic north for one, and 50 degrees
> off of magnetic north for the other).
>
> This would be simple to plot to get a position on a
> map. The question is: is this a mathematically
> solveable problem?
>
> If so, what is the formula?
>
> Thanks in advance for your help!
>
> Regards,
>
> Rene Schmidt
>
> __________________________________
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>
> Dave Weilacher
> .US Coast Guard licensed captain
> .    #889968
> .ASA instructor evaluator and celestial
> .    navigation instructor #990800
> .IBM AS400 RPG contract programmer
>

   

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