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Math Help - Need help creating a formula

  1. #1
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    Need help creating a formula

    I need to create a formula for excel that will solve the problem depicted in the drawing. Any help is appreciated.
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  2. #2
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    Quote Originally Posted by T6902ws View Post
    I need to create a formula for excel that will solve the problem depicted in the drawing. Any help is appreciated.
    I've modified your drawing a little bit.

    As you can see you are dealing with 2 right triangles. x is the difference of 2 legs of the 2 triangles.

    I don't know excel. But I can provide you with an OpenOffice spreadsheet ...
    Attached Thumbnails Attached Thumbnails Need help creating a formula-sekant_stueck.png  
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  3. #3
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    I understand the logic, I would like to see the open office formula.
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  4. #4
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    Quote Originally Posted by T6902ws View Post
    I understand the logic, I would like to see the open office formula.
    I've attached a screen-shot of the spreadsheet:

    R1 := radius of the outer circle
    R2 := radius of the inner circle
    d := length of the secant (with your example 30)

    The formula is shown in the input line. Translate the word wurzel by sqrt (Wurzel is the German word for root)

    I hope that this helps!
    Attached Thumbnails Attached Thumbnails Need help creating a formula-sekant_stueckcalc.png  
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  5. #5
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    according to the attached pic:

    x + y = 30
    y = 30 - x .....(1)
    By Pythagarus Theorem.:
    33^2 - (x + y)^2 = z^2
    30^2 - y^2 = z^2
    Hence
    33^2 - (x + y)^2 = 30^2 - y^2
    33^2 - 30^2 = (x + y)^2 - y^2
    189 = x^2 + 2xy + y^2 - y^2
    x^2 + 2xy = 189 .....(2)
    (1) to (2), hence:
    x^2 + 2x(30 - x) = 189
    x^2 + 60x - 2x^2 - 189 = 0
    -x^2 + 60x - 189 = 0
    x^2 - 60x + 189 = 0
    x = [-(-60) +/- (60^2 - 4 x 1 x 189)^0.5] / (2 x 1)
    x = 56.66 (rejected)
    or
    x = 3.34
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  6. #6
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    Quote Originally Posted by ukorov View Post
    according to the attached pic:

    x + y = 30 <<<<<<< in my opinion this assumption doesn't hold for all values of z
    ...
    x is the difference of the two green lines.
    Attached Thumbnails Attached Thumbnails Need help creating a formula-sekant_stueckfalsch.png  
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  7. #7
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    Quote Originally Posted by earboth View Post
    x is the difference of the two green lines.
    alright i am now aware of the problem. however x is not the difference of the two green lines either, because the question has never given that x + y is precisely equivalent to the length of the inner radius (30).

    To ignore this arguement, we only use the Pyth. Th. twice:
    (x + y)^2 + 15^2 = 33^2
    (x + y)^2 = 33^2 - 15^2
    x^2 + 2xy + y^2 = 864 .....(1)
    y^2 + 15^2 = 30^2
    y^2 = 675
    y = (5)(27^0.5) .....(2)

    (2) to (1) we have:
    x^2 + 2x(5)(27^0.5) + 675 = 864
    x^2 + (10)(27^0.5)x - 189 = 0

    x = [-(10)(27^0.5) +/- (2700 + 4 x 189)^0.5] / 2
    x = 3.41
    or
    x = -55.4 (rejected)
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  8. #8
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    The correct answer is 3.41.

    Thanks
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