anonymous
  • anonymous
What is the measure of the two other sides of a 45-45-90 degree triangle, with a 2 square root of 6 hypotenuse?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@zepdrix help please or tell me how to solve this :^o
zepdrix
  • zepdrix
|dw:1450049846596:dw|This is similar to the last problem. In a 45-45-90, the "legs" are the same length.
zepdrix
  • zepdrix
Pythagorean Theorem should clean it up from there :O

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anonymous
  • anonymous
x^2 + x^2 = 2 square root of 6?
Owlcoffee
  • Owlcoffee
That is correct, since two angles composed by one common side are equal, this must imply that the triangle we are looking is an "isoceles triangle" therefore the segments composinf the final vertex are congruent as well. Translating this to the pythagorean theorem: \[x^2+x^2=2\sqrt{6} \iff (2)x^2=2\sqrt{6}\] Can you take over from here?
anonymous
  • anonymous
I tried so, and got that the two other sides equal 6? I'm wrong, aren't?
Owlcoffee
  • Owlcoffee
let's give it a shot: \[2x^2=2\sqrt{6} \iff x^2=\sqrt{6} \iff x=\sqrt{\sqrt{6}}\]
anonymous
  • anonymous
Is \[\sqrt{\sqrt{6}}\] the answer then :^o
Owlcoffee
  • Owlcoffee
Yes, since \(\sqrt{\sqrt{6}}\) already represents an irrational number which means the sides do have that length. You can also simplify using exponential properties: \[\sqrt{\sqrt{6}} \iff ((6)^{\frac{ 1 }{ 2 }})^{\frac{ 1 }{ 2 }} \iff (6)^{\frac{ 1 }{ 4 }} \iff \sqrt[4]{6}\] But you can leave it as \(\sqrt{\sqrt{6}}\) since it looks nicer like that ;)
anonymous
  • anonymous
Thank you so muchhhhh omg

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