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 \(1\).
I'm really stuck, can someone help? thanks
+161 If DG is at most 1, we can draw a circle with radius 1 and center D.
We know the circle and triangle will share a 60 degree sector.
So the area of the sector is pi/6.
The area of the entire equilateral triangle is sqrt3/4*a^2, and since a=3, 9sqrt3/4.
3.8971 is the approximate area of the triangle, and 0.5236 is the approximate area of the sector.
So 0.5236/3.8971 which is around 0.134356
-tigernathan
