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

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

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
By 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... \(2e^2 = e^2 + e^2\) \(2e^2 = (a^2  b^2) + (c^2  d^2)\) \(\displaystyle e^2 = \frac{a^2 + c^2  (b^2 + d^2)}{2}\) \(\displaystyle e = \sqrt{\frac{a^2 + c^2  (b^2 + d^2)}{2}}\)
 2 years ago

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

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.0
I 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?
 2 years ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
Hm, 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...
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.0
But 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.
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.0
Apparently 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"
 2 years ago
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