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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

 Aug 5, 2020
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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

 Aug 5, 2020
edited by tigernathan  Aug 5, 2020

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