Find the Intersection of the Lines

Date: 10/21/2002 at 20:11:59
From: Linda
Subject: Trig 

If two poles 10m and 15m high are 25m apart, what is the height of 
the point of intersection of the lines that run from the top of each 
pole to the foot of the other pole?

Date: 10/21/2002 at 22:47:26
From: Doctor Ian
Subject: Re: Trig 

Hi Linda,

Here is a picture, where A is the top of one pole, and B is the top 
of the other. 

    20 -
       |
    15 -                        B
       |                        .
    10 A                        .
       .                        .
     5 .                        .
       .                        .
       +----|----|----|----|----|----
            5   10   15   20   25

The first line runs from (0,10) to (25,0).  The second line runs from 
(0,0) to (25,10). 

From two points on a line, you can find the equation of the line.  
From the equations of two lines, you can find the intersection of the 
lines by setting 

        y = y'
 
   mx + b = m'x + b'
 
and solving for x. 

Can you take it from here? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/