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

 Jan 8, 2020
edited by Melody  Jan 8, 2020

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!


 Jan 8, 2020

what is that in fraction form?

Guest Jan 9, 2020

Don't be so lazy and work it out yourself!


What happened to 'Thanks very much'   That would have been an appropriate response!

Melody  Jan 9, 2020

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