Results 1 to 3 of 3

Math Help - Equilateral shaped dartboard has a circle in it. probability of dart hitting the circ

  1. #1
    Newbie
    Joined
    Jun 2011
    Posts
    1

    Equilateral shaped dartboard has a circle in it. probability of dart hitting the circ

    This is an IGCSE probability question that is giving me a lot of trouble. Since it's not just a probability problem and that the non probability part is the part giving me trouble I decided to put it here.

    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).

    A) Given that tan 60 degrees = \sqrt{3} and sin 60 degrees =
    \sqrt{3} /2

    show that the probability of the dart hitting the board inside the circle is
    \pi /3 \sqrt{3}

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


    My working:
    The probability should be the area of the circle (\pi r^2) over the area of the triangle(half* unknown base * unknown height)

    So you should somehow end up with \pi r^2/ 3r^2 \sqrt{3} which simplifies down to \pi /3 \sqrt{3}

    But how do use the information in the question to find out that the area of the triangle is 3r^2\sqrt{3} ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    Find the center of the circle.
    From this center, draw the three radii perpendicular to the three sides of the triangle.
    From this center, draw the three line segments to the vertices of the triangle.

    There's a whole lot of information in that structure.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,669
    Thanks
    1618
    Awards
    1
    Quote Originally Posted by Paul82 View Post
    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).
    Suppose that the length of a side of the equilateral triangle is \mathbf{s}.
    Then the area is \mathcal{A}=\frac{\sqrt{3}\mathbf{s}^2}{4}.

    The radius of the inscribed circle is \mathbf{r}=\frac{\sqrt{3}\mathbf{s}}{6}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. equilateral triangle inscribed in a circle..
    Posted in the Geometry Forum
    Replies: 4
    Last Post: February 28th 2010, 09:52 PM
  2. Equilateral Triange inside a circle
    Posted in the Geometry Forum
    Replies: 7
    Last Post: February 16th 2010, 10:20 PM
  3. Dart Board Probability
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 28th 2009, 01:53 PM
  4. Equilateral Triangle Inscribed in Circle
    Posted in the Geometry Forum
    Replies: 2
    Last Post: January 23rd 2007, 02:35 AM
  5. Equilateral Triangle & Circle
    Posted in the Geometry Forum
    Replies: 2
    Last Post: January 23rd 2007, 02:31 AM

Search Tags


/mathhelpforum @mathhelpforum