help probability

 

Let DEF be an equilateral triangle with side length 3. At random, a point G is chosen inside the triangle. Compute the probability that the length DG  is less than or equal to 2  

 

 

Draw DEF, equilateral triangle with side length 3. 

Put the point of your compass on D and draw a circle with radius 2. 

 

If DG is within the segment of the circle that's inside the triangle, it will be 2 or less. 

If DG is outside the segment of the circle that's inside the triangle, it will be more than 2. 

 

Figure the area of the segment inside the triangle.  A_Segment     I got 2.09  (I called it 60/360 of the whole circle.)  

Figure the area of the entire triangle.                      A_Triangle       I got 3.90  (I used sin(60^o) to calculate the altitude.)  

 

Divide A_Segment by A_Triangle.  The quotient is the probability.  2.09 / 3.90  =  0.54