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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)

    The area of the circle is
    The probability of falling inside the circle and outside the triangle is therefore

  • 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 -

    I get
    P(C\T) (probability inside circle minus triangle)

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