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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Guest Jan 8, 2020

#1**0 **

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%.

You are very welcome!

:P

CoolStuffYT Jan 8, 2020