Math Help!

The radius of this circle is one unit.

Find the exact lengths of the legs in the right triangle if:

Sides a is twice as long as side b.

And Sides b is twice as long as side a.

Basically the hypotenuse of this triangle is 1 and we are trying to use the pythagorean theorem to find the lengths of side a and b according to the terms described above.

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  1. if b=2a, then

    a^2 + (2a)^2 = 1
    5a^2 = 1
    a = 1/√5

    similarly for a=2b

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  2. first case 1: a = 2b

    so a^2 + b^2 = 1^2
    (2b)^2 + b^2 = 1
    5b^2 = 1
    b^2 = 1/5
    b = 1/√5
    one side is 1/√5, the other is 2/√5

    you do case 2

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