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asnaseer

  • 2 years ago

Geometry challenge. Question to follow in drawing.

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  1. asnaseer
    • 2 years ago
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    |dw:1328465419159:dw|

  2. asnaseer
    • 2 years ago
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    there are 3 squares next to each other. prove C = A + B

  3. Mr.Math
    • 2 years ago
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    3 squares with the same side length I presume?

  4. asnaseer
    • 2 years ago
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    yes - 3 identical squares

  5. asnaseer
    • 2 years ago
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    BTW: This is a geometry challenge - so no trig allowed :)

  6. FoolForMath
    • 2 years ago
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    Okay I can solve it using height and distance, one interesting fact: \( \sin(C-B) = \sin (C) \sin (B) \)

  7. FoolForMath
    • 2 years ago
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    Snap! asnaseer :P

  8. Mr.Math
    • 2 years ago
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    Oh man, this sucks!

  9. asnaseer
    • 2 years ago
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    :D - think "outside" the box

  10. FoolForMath
    • 2 years ago
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    Comone why not use trig? :P

  11. asnaseer
    • 2 years ago
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    ok - lets see the trig solution. but there is a very elegant geometric solution if you can find it. :)

  12. FoolForMath
    • 2 years ago
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    Hmm Asnaseer rules :D

  13. asnaseer
    • 2 years ago
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    I'm off to have some food - will be back soon ...

  14. Mr.Math
    • 2 years ago
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    I can't seem to be able to find a geometrical proof. Here's a proof using trigonometry: We have \(\sin C=\frac{1}{\sqrt{2}}\), \(\sin B=\frac{1}{\sqrt{5}}\), \(\sin A=\frac{1}{\sqrt{10}}\), and \(\cos A=\frac{3}{\sqrt{10}}\), \(\cos B=\frac{2}{\sqrt{5}}.\) It's easy to show that \(\sin C=\sin(A+B)\) and hence \(C=A+B \text{ because } A,B, C \in (0, \frac{\pi}{2}).\)

  15. asnaseer
    • 2 years ago
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    I'll let this problem /simmer/ for a while before showing the geometric proof - unless of course someone actually proves it by then :)

  16. moneybird
    • 2 years ago
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    any hints?

  17. asnaseer
    • 2 years ago
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    I gave a hint above - think "outside" the box :)

  18. asnaseer
    • 2 years ago
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    I guess I can give another hint to you guys, here it is...

  19. asnaseer
    • 2 years ago
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    |dw:1328468434372:dw| essentially, you want to try and prove that D=B

  20. Shayaan_Mustafa
    • 2 years ago
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    It can be proof using Euclidean concepts of geometry i.e. using theorems, postulates, axiom etc... It is actually difficult. But intresting.

  21. asnaseer
    • 2 years ago
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    There is actually a much easier proof using only the properties of similar triangles.

  22. Shayaan_Mustafa
    • 2 years ago
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    Yes I know in terms of Euclidean Geometry. These properties of triangles are followed by, called, postulates.

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