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geometry

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A 30-60-90 triangle is inscribed in a circle. The length of the hypotenuse is 12 inches. If a coin is tossed on the figure, what is the probability that the coin will land in the circle, but outside the triangle?

  • geometry -

    All right-triangles inscribe in a circle with a diameter equal to the hypotenuse.

    Therefore for the 30-60-90 triangle, the radius of the circle is 6 inches, and the short side is also 6 inches. The height is 6sqrt(3), so the area of the triangle is
    At=36sqrt(3)/2 = 18 sqrt(3) sq.in.

    The area of the circle is
    Ac=π6^2=36π
    The probability of falling inside the circle and outside the triangle is therefore
    P(C\T)=(Ac-At)/Ac

  • geometry -

    the quesiton is land in the circle, but outside the triangle. Is it the probability is (AC - AT)/AC
    81.22/113 x 100%
    = 72%

  • geometry -

    Correct.
    I get
    P(C\T) (probability inside circle minus triangle)
    =(Ac-At)/Ac
    =81.92/113.1=72.4%

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