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Unformatted text preview: = 1/G. Pythagoras’s Theorem gives the relationships 1 + F 2 = (3.5 + D) 2 and 1 + G 2 = (3.5  D) 2 F 2 = (4.5 + D)(2.5 + D) and G 2 = (4.5  D)(2.5  D) Multiply these last equations together and use F = 1/G to get 1 = (20.25  D 2 )(6.25  D 2 ) which yields a quadratic equation in D 2 . The rest is straightforward. The height of the ladder is [IMAGE] William Webb’s solutions is trigonometric in nature. Start by labeling the lower right hand angle A. The distance from C to B is csc(A) while that from C to T is sec(A). He now uses various trig identities to show that sin(2A) is a root of the quadratic equation 49x 2 4x  4 = 0. The rest follows easily. to this page....
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 Spring '10
 AlbertoDelgado
 Combinatorics, Equations, Quadratic equation, Elementary algebra, Indian mathematics, Greg Falcon, William Webb

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