+295 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 ?
+4609 Hint: .( target area of triamgle) / (whole area of triangle) = desired probability
+128475 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%
