Results 1 to 2 of 2

Math Help - ladder problem

  1. #1
    Junior Member
    Joined
    Oct 2012
    From
    London
    Posts
    46

    ladder problem

    There are 2 ladders, one is 25 ft long the other is 20 ft long, they are crossing eachther in an alley between two buildings, find the distance between the two buildings. The point where the ladders intersect to the ground is 10 ft.

    ladder problem-untitled.png
    Please help, thanks in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: ladder problem

    I would let the width of the alley be x, where 0<x. Drop a vertical line down from the point where the ladders meet to the ground. Let the horizontal distance from the left wall to the vertical line be x_1 and the horizontal distance from the vertical line to the right wall be x_2, hence:

    x_1+x_2=x

    Now, by similarity (and the Pythagorean theorem), we find:

    x_1=\frac{10x}{\sqrt{20^2-x^2}}

    x_2=\frac{10x}{\sqrt{25^2-x^2}}

    Now solve for x.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. The problem of the ladder!
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: May 3rd 2011, 06:51 PM
  2. Sliding ladder problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 31st 2010, 07:22 PM
  3. A ladder problem...
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 1st 2009, 02:04 PM
  4. Help with ladder triangle problem
    Posted in the Geometry Forum
    Replies: 3
    Last Post: July 5th 2009, 10:13 PM
  5. Challenging Ladder Problem
    Posted in the Geometry Forum
    Replies: 1
    Last Post: February 17th 2008, 06:03 PM

Search Tags


/mathhelpforum @mathhelpforum