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Simplifying this equation

  1. Apr 26, 2012 #1
    1. The problem statement, all variables and given/known data
    Is it possible to simplify this even further?
    28b4d3b.jpg

    2. Relevant equations
    This is a Secant-tangent equation.
    Secant: AD = 18/radical 3 AC = ??

    3. The attempt at a solution
    I cross multiplied to get 18=324radical 3 (AC)
    and in the end i got 0 = (18radical3) (AC) which makes no sense

    so is there a different way to simplify that?
     
  2. jcsd
  3. Apr 26, 2012 #2

    Mark44

    Staff: Mentor

    Are you trying to solve for AC?
    When you divide both sides by 18, you will be left with 1 on the left side, not 0.

    If you are trying to find AC, divide both sides by 324√3.
     
  4. Apr 26, 2012 #3
    Yes.
    Here is the original question
    dh09i.jpg
     
    Last edited: Apr 26, 2012
  5. Apr 26, 2012 #4

    Mark44

    Staff: Mentor

    It doesn't seem to me that you have enough information.

    How did you go from AB = 18 and AD = 18/√3 to 18 = 324√3 * AC?
     
  6. Apr 26, 2012 #5
    I'm really terrible at maths...that's why I'm here.
     
  7. Apr 26, 2012 #6

    Mark44

    Staff: Mentor

    Draw a radius from O to B, and call its length r. The radius OB is perpendicular to AB, so that ABO is a right triangle.

    Let θ = the angle at A.

    Then, from your given information,

    cos(θ) = 18/(r + 18/√3), and
    sin(θ) = r/(r + 18/√3)

    Now you have two equations in two unknowns, so you should be able to solve for both unknowns, although you only need r. Once you know r, it's pretty easy to get AC.
     
    Last edited: Apr 26, 2012
  8. Apr 26, 2012 #7
    Start out like Mark44 said by drawing a radius from O to B, and call its length r, but then apply the Pythagorean Theorem to the right triangle ABO to find r.

    Chet
     
  9. Apr 27, 2012 #8

    Mark44

    Staff: Mentor

    That's simpler than what I suggested. Simple is good!
     
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