Question

Given the circle with radius 12, what is the probability of choosing a point inside the triangle?

Answer 1

.14
.21
.79
.86

Answer 2

Alright, so the total area of the circle is \[A=\pi r^2 = \pi (12)^2=452.389\]the size of the triangle can be found using a bit of trig \[\sin(60^o)=x/12\]where x is half the length of the bottom of the triangle\[x=12sin(60^o)=10.39\]therefore the length of the bottom is 20.78

The height of the triangle is also found using trig and is equal to \[\cos(60^o)=y/12\]\[y=12cos(60^o)=6\]Now, the total area of the triangle is 6 * 20.78 * .5 = 62.34
Divide the two and you have your answer: 62.34/452.389 = .137 = .14

Answer 3

alritey thanks :)