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Triangle  abc is equilateral with side length 3. A point x is randomly chosen within abc . What is the probability that x is no more than 1 unit away from vertex a ?

 
Darkside  Sep 11, 2018
 #1
avatar+3011 
+2

Hint: .( target area of triamgle) / (whole area of triangle) = desired probability 

 
tertre  Sep 11, 2018
 #2
avatar+88830 
+1

If we center a circle with a radius of 1 at "A"...the area of the circle  sector contained by the triangle will be :

 

 pi * (1)^2  (60 / 360)  =    pi/ 6  ....   (1)

 

And the area of the triangle is   (1/2)(3)^2 sqrt (3)/2   =  9sqrt(3)/4   .....(2)

 

So.....the  probability is  (1) / (2)   =  [  pi/6 ]  / [ 9 sqrt (3) / 4 ]   ≈  13.44%

 

 

cool cool cool

 
CPhill  Sep 11, 2018

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