Need help creating a formula

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October 30th 2009, 12:42 PM
T6902ws

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.
http://www.smugmug.com/photos/697613115_NMf4q-XL.jpg
October 30th 2009, 12:52 PM
earboth

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Quote:

Originally Posted by T6902ws

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 ... (Nod)
October 30th 2009, 12:58 PM
T6902ws

I understand the logic, I would like to see the open office formula.
October 30th 2009, 01:22 PM
earboth

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Quote:

Originally Posted by T6902ws

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!
October 30th 2009, 08:08 PM
ukorov

1 Attachment(s)

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
October 31st 2009, 02:27 AM
earboth

1 Attachment(s)

Quote:

Originally Posted by ukorov

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.
October 31st 2009, 08:51 AM
ukorov

Quote:

Originally Posted by earboth

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)
November 2nd 2009, 07:40 AM
T6902ws

The correct answer is 3.41.

Thanks