Puzzle time - Find the angle
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@jon-nyc said in Puzzle time - Find the angle:
Sorry - the two shaded triangles are equilateral.
But that alone is not enough. For instance, I could shrink one of the triangles by 50% and change the angle. You'd need something else like "the area of the bigger one is twice the area of the smaller".
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Definitely there is a solution
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No cheating and saying ‘since it’s true for any relative size triangles let me assume they’re the same size and figure out that special case’.
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Can you prove it?
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Well, I assume if I set up a formula for the angle given side length a and b for the triangles, then simplify using textbook identities for trigonometric functions, the a's and b's will magically cancel each other all out and I'll just get the 120 degrees.
There should be a tool online that turns geometric constructions into algebraic equations. There's pizza in the oven, so I can't be bothered to do that by hand right now
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I'm going with 120 degrees.
My reasoning is that Klaus knows about this stuff.
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Sorry, I should probably have put that in a spoiler
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You can do it without complex trig identities. In your head in fact.
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Not quite right but the solution is that ‘simple’.
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My answer:
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Ok. Angles 1 and 2 summed together obviously = 180 degrees, but then so do 2 and 3.
If 1+2=180, and 1+3=180, then 2=180-1 and 3=180-1 so 1 and 3 are equal.
