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Sin Rule & Pythagoras?

  1. Jan 25, 2009 #1
    1. The problem statement, all variables and given/known data
    The two sides of a stepladder are of length 2m and 1.85m. When fully opened, the longer side is inclined at 65° to the horizontal. Find the distance apart of the feet of the step ladder.

    2. Relevant equations
    Sin Rule & Pythagoras?

    3. The attempt at a solution
    I had a go but I really think it's wrong.


    [itex]\frac{2}{\sin90°} = \frac{b}{\sin65°}[/itex]

    [itex]b = \frac{2}{\sin90°}\times \sin65°[/itex]

    [itex]b = 1.81 (2d.p.)[/itex]

    [itex]a^2 = 2^2 - 1.81^2 = 0.7239[/itex]

    [itex]a = 0.85 (2d.p.)[/itex]

    [itex]x^2 = 1.85^2 - 0.85^2 = 2.7[/itex]

    [itex]x = 1.64 (2d.p.)[/itex]

    [itex]l = 1.81 + 1.64 = 3.45m[/itex]

    P.S. How do you do new lines in LaTeX?
  2. jcsd
  3. Jan 25, 2009 #2
    Re: Ladder

    How do you know that the top angle is 90 degrees when it is fully opened? I think you have to stick with just the 65 degree angle and the leg lengths in order to find the distance.

    Also, I don't know how to do new lines in LateX. I always just close the tex tag and start a new one.
  4. Jan 26, 2009 #3
    Re: Ladder

    I thought it would be 90 degrees because it says 65 degree to the horizontal.
  5. Jan 26, 2009 #4
    Re: Ladder

    You cant assume that the ladder opens up at 90 degrees (it doesnt actually).
  6. Jan 26, 2009 #5
    Re: Ladder

    I see what I did wrong. I got horizontal and verticle mixed up so I drew my diagram wrong.
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