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  • 22-03-2019
  • Mathematics
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in a right triangle with the hypotenuse c and the legs a and b, c^2=2ab. find the measure of each acute angle.

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Аноним Аноним
  • 22-03-2019

We know that, usually,

[tex] c^2 = a^2+b^2 [/tex]

In this case, we also know that

[tex] c^2 = 2ab [/tex]

We deduce that

[tex] a^2+b^2 = 2ab [/tex]

If we subtract 2ab from both sides, we get

[tex] a^2-2ab+b^2 = 0 \iff (a-b)^2 = 0 \iff a=b [/tex]

So, the triangle is an isosceles right triangle, and so the angles are 90-45-45

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