An IGCSE Geometry/Probability question

[vito_corleone]

A dartboard is in the shape of an equilateral triangle inside which is inscribed a circle.
A dart is randomly thrown at the board (Assume that it hits the board).

Given that tan 60° = sqrt(3) , and sin 60° = sqrt(3)/2, show that the probability of the dart hitting the board inside the circle is π/ 3* sqrt(3).

The probability should be the area of the circle divided by the area of the triangle , and you should end up with π/ 3* sqrt(3).

But how do you end up with that starting from scratch, as I end up with a different answer , when I solve it?

Thanks in advance.

The diagram given looks like this :- http://tinyurl.com/3nym92q

 

[stapel]

A dartboard is in the shape of an equilateral triangle inside which is inscribed a circle.
A dart is randomly thrown at the board (Assume that it hits the board).

Given that tan 60° = sqrt(3) , and sin 60° = sqrt(3)/2, show that the probability of the dart hitting the board inside the circle is π/ 3* sqrt(3).

The probability should be the area of the circle divided by the area of the triangle , and you should end up with π/ 3* sqrt(3).

But how do you end up with that starting from scratch, as I end up with a different answer , when I solve it?

We'll be glad to help you find any errors, but we'll first need to see what you've tried. Please reply with a clear listing of your efforts so far. Thank you!