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inkyvoyd
 4 years ago
Simple geometry
inkyvoyd
 4 years ago
Simple geometry

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inkyvoyd
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1352774312422:dw how does one express

inkyvoyd
 4 years ago
Best ResponseYou've already chosen the best response.0e in terms of a, b, c, and d?

AccessDenied
 4 years ago
Best ResponseYou've already chosen the best response.1By Pythagorean Theorem: \(b^2 + e^2 = a^2\), \(d^2 + e^2 = c^2\) Solving for \(e^2\) in both cases: \(e^2 = a^2  b^2\) \(e^2 = c^2  d^2\) I guess one way we could do so is by simply adding the equations together... \(2e^2 = e^2 + e^2\) \(2e^2 = (a^2  b^2) + (c^2  d^2)\) \(\displaystyle e^2 = \frac{a^2 + c^2  (b^2 + d^2)}{2}\) \(\displaystyle e = \sqrt{\frac{a^2 + c^2  (b^2 + d^2)}{2}}\)

inkyvoyd
 4 years ago
Best ResponseYou've already chosen the best response.0Question, if a and c were known, but only b+d was known, how would one solve htis problem?

inkyvoyd
 4 years ago
Best ResponseYou've already chosen the best response.0I mean, say that you had 3 sides of a triangle, and drew a given altitude, what would be the two lengths of the resulting split side?

AccessDenied
 4 years ago
Best ResponseYou've already chosen the best response.1Hm, I think we would have to find e in terms of a and c using angles (found by law of cosines). I don't think it would be solvable with that particular equation only since you'd only have two equations for three unknowns there: e, b, and d...

inkyvoyd
 4 years ago
Best ResponseYou've already chosen the best response.0But it would be solvable  draw any triangle right now, and you can measure the sides  now draw an altitude to any single side  you have just created the problem.

inkyvoyd
 4 years ago
Best ResponseYou've already chosen the best response.0Apparently I can do this with heron's theorem and the pythagorean theorem, but I was wondering if there are a few lines or simple algebraic manipulations I could make to get it done easily. http://en.wikipedia.org/wiki/Altitude_(triangle) wher it says "altitude in terms of the sides"
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