Grex Iq Conference

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Grex Iq Item 144: NEW!!-Three trees and a river puzzle.(Trigonometry)
Entered by koolfire on Sat Mar 4 22:29:57 UTC 2000:

This is a puzzle from my friend at my college. Was quite interesting and i
thought..it was worth posting. Have fun solving it. Real interesting one.
There is a river and on either side(bank) there is a tree(i've shown the
pictorial representation below). There is another tree on one bank of the
river a certain distance away from one of our trees so that the structure of
these three trees forms a right-angled trianglewith the height being the width
of the river and the base being the distance between the trees on the same
side of the river. Consider this setup on an island and an inhabitant of this
island knows the distance between the two trees on the same side of the river
in "number of steps" he can take. You have to tell me how the inhabitant can
find out the width of the river... i.e the height of the rt-angled triangle.
The solution involves a little bit of trigonometry to be applied. Nevertheless
it is quite easy.. The stars indicate the trees on either side f the river
and the lines indicate the river itself.
RESTRICTIONS: No use of ropes or ruers or any measuring apparatus. No crossing
the river(obviously!!)
        *
-------------------------------------------------------







-------------------------------------------------------
       *                      *

As you can see the stars form rt-angled triangle. Determine the method by
which the width of the river(dist betw the vertical stars) can be determined.
If noone comes up with a good answere i'll post the result in a few days. Bye!

3 responses total.

#1 of 3 by rcurl on Mon Mar 6 19:44:43 2000:

I presume we can't measure an angle and use trig functions, but can we
measure in "paces" (that's a measuring apparatus - legs - so I thought
I'd better ask). 

If I can "pace", I would pace to bisect the base, and then walk away
from the river from the point at the acute angle until I line up
with the bisection and the tree on the other side. I will then be
the width of the river away from the river.

#2 of 3 by koolfire on Fri Mar 10 02:44:20 2000:

yes rane curl.... you got it right. you walk away from the dirn. of the river
from the second pint in the base and then look back to the mid pt of the base
and if the mid-pt and the tree on the other side of the river coincide in one
line then the distance you have walked is the distancce between the trees on
the opposite banks. Good going Rane!!

#3 of 3 by aruba on Tue Jun 20 16:03:46 2000:

Good problem!

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