Solve for n.


|
|\
| \
| \5+n
y| \
| \
|__2__\
| |\
2| 2| \5-n
|_____|__\___
2 x

Using the Pythagorean theorem:

x^2 = (5-n)^2 - 4 = n^2 - 10n + 21
y^2 = (5+n)^2 - 4 = n^2 + 10n + 21


Using rule of similar triangles:

y/2 = 2/x
yx = 4
y^2 * x^2 = 16
(n^2 - 10n + 21) * (n^2 + 10n + 21) = 16
n^4 - 58n^2 + 425 = 0


Solving quadratic equation:

ax^2 + bx + c = 0


x = (-b + Sqrt(b^2 - 4ac))/2a = 49.396

x = (-b - Sqrt(b^2 - 4ac))/2a = 8.604

x = n^2

n = srqt(49.396) or n = sqrt(8.604)

n = 7.0282287953651594252678749478686 (Damn, this can't be right!)

or

n = 2.9332575747792760110661745961244 (Hmmm, maybe)


y^2 = (5+n)^2 - 2^2

y^2 = 7.9332575747792760110661745961244^2 -4

y^2 = 58.936575747792760110661745961237

y = 7.6770160705701769496450099398666

y+2 = 9.6770160705701769496450099398666 ft.

y+2 = 116.1241928468421233957401192784 in.

What a headache.



--
Steve Walker
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