# geometry

posted by .

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%

## Similar Questions

1. ### geometry

The radius of the inscribed circle is equal to twice the area of the triangle divided by the perimeter of the triangle. Prove that this relationship is true for the inscribed circle in any right triangle.
2. ### geometry

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?
3. ### Geometry

If a circle with center O has equilateral triangle AOB inscribed with sides 10 inches long. If OC is perpendicular to AB at P, what is the length of AP in inches?
4. ### math

a fair coin is tossed in the air 4 times. if the coin lands heads up the first three tosses, what is the probability the coin will land heads up the fourth toss?

1.An isosceles triangle with each leg measuring 13 cm is inscribed in a circle . if the altitude to the base is 12 cm find the radius of the circle 2. Circles a and b are tangent at point c. p is on circle a and q is on circle b such …
6. ### GEOMETRY CIRCLE

1.An isosceles triangle with each leg measuring 13 cm is inscribed in a circle . if the altitude to the base is 12 cm find the radius of the circle 2. Circles a and b are tangent at point c. p is on circle a and q is on circle b such …