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?

Answer 1

if a right triangle is inscribed in a circle, the hypotenuse is a diameter of the circle.

so, circle radius is 6

area of circle = 36pi
area of triangle 6*6sqrt(3)

p(outside) = 1-sqrt(3)/pi = .45