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Puzzles Euclids Triangle You might need to remember a few of the things Euclid taught you about triangles.
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Euclid has a triangle in mind. Its longest side has length 10 and another of its sides has length 7. It's area is 20. What is the exact length of its third side? (Your answer will have some square roots in it!)
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Comments | terveloc |  13:39:41, 17 Nov 07 |  Newbie
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| I approached the problem differently than Danik, but got the same answer. From a complex vectors approach, the final equation gives,
x = abs(10-7*exp(i*arcsin(40/70))).
This simplifies to sqrt(149-20*sqrt(33)).
| | | | Danik | 16:48:55, 10 Oct 07 | Newbie
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| Call the height perpendicular to the side of length 10 h. Then you have 20=10*h/2 <=> h=4
Then use pythagoras theorem on the left triangle with sides 7 and h to get length of the bottom left side you get when splitting the side of length 10 where h is. Call it a.
a^2+h^2=7^2 <=> a=sqrt(33)
Call the other part of the side of lenght 10 b. You then have
h^2+b^2=x^2, where x is the length of the wanted side.
x=sqrt(149-20*sqrt(33))
| | | | Jackson | 18:25:43, 09 Oct 07 | Newbie
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| root of 83, this is rather involved, and requires a figure to explain why it works, im me on yahoo at jellyfishshad for how to work it out
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