Three Tapers and a Length

Date: 8/25/95 at 21:7:27
From: Anonymous
Subject: Three tapers and a length

Dr. Math,
I am a reasonably young guy but I have never had much schooling 
in geometry.  I have a problem and I was wondering if it could 
be figured out.

I have three tapers (or angles) that intersect with each other. 
I will attempt to make a drawing here:

       X*
            *
                *
                    *A
                       *
                          *
                             *
                    D          *B
                                 *
       O                           *Y

The angle from X to A is 30 deg
The angle from A to B is 40 deg
The angle from B to Y is 50 deg

Theoretically, if I were given the total length from O to Y 
and the total height O to X and of course the three angles, 
is it possible to calculate each angle's length and height?

In other words like the length B to D and the height D to A. 
I feel like I would need more information to calculate these 
values but I am not sure.

Any ideas?

Larry

Date: 8/27/95 at 15:9:23
From: Doctor Ken
Subject: Re: Three tapers and a length

Hello!

No, I'm afraid there isn't one definite solution to this problem.  
In fact, A and B could be at lots and lots of different places.  
I've made a sketch using The Geomteter's Sketchpad, and it's 
sitting at 

http://mathforum.org/dr.math/sketches/tapers.gsp     

If you don't have a copy of the program, you can download a 
demo copy of it which will let you view the sketch.  You can 
do the downloading from 

http://mathforum.org/dynamic.html   .  

Good luck!

- Doctor Ken,  The Geometry Forum