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Math Help - Isosceles Triangle

  1. #1
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    Isosceles Triangle

    Hey Guys!

    Just to be sure. I don't know if I am correct since I can't view the answer on the back of the book

    An isosceles right triangle has a hypotenuse of length
    10 cm. How long is each leg?










    So I have an isosceles triangle

    one 90 degree angle and two angles with the same measure.

    hypotenuse is 10 so i assume 10^2 = 100

    others are 5√2 (bootleg radical sign) I think since I have the hypotenuse of a 45 45 degree right angle has a base of x and hypotenuse x√2.

    Not sure if this is correct.
    Last edited by Cake; November 6th 2013 at 11:54 PM.
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  2. #2
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    Re: Isosceles Triangle

    yup, there's a couple ways to do this, both based on the Pythagorean formula.

    A^2+B^2=C^2

    where C is the hypotenuse, A and B are the legs.
    But, since the triangle is isosceles, A=B, so

    2*A^2=C^2
    substituting...
    2*A^2 = (10)^2 = 100
    A^2 = 50 = 25*2
    A= 5*sqrt(2)

    or, if you happen to know that the sides of a 45-45-90 triangle have the ratio 1:1:sqrt(2), you can jump straight to
    A*sqrt(2) = 10
    A = 10/sqrt(2) = 5*sqrt(2)
    Thanks from Cake
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  3. #3
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    Re: Isosceles Triangle

    Perfect, got it.
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