Let triangle DEF be equilateral, where the side length is 3. Point G is chosen at random inside the triangle. Find the probability that the length DG is at most 1.
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~ Melody
+1252 First one.
If DG is at most one, we can draw a circle with radius 1 and center D.
We know the circle and triangle will share a 60 degree sector (because equilateral triangles have angle 60 degrees each).
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 approx. area of triangle
0.5236 is the approx. area of sector.
So 0.5236/3.8971 is around 0.134356
Or 13.4356%.
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