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Obtuse angle? (Posted on 2017-10-25) Difficulty: 3 of 5
Fix a line segment L in the plane.
Among all triangles which have L as longest side one is chosen at random.

What is the probability it is obtuse?

No Solution Yet Submitted by Ady TZIDON    
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pi/2 - 1

Let L=1. x and y and the other legs. Then x<=1, y<=1, which is the unit square in the first quadrant. The triangle is obtuse if and only if x^2 + y^2 < 1, which means (x, y) is within the circle in the first quadrant. 

But to form a triangle, x+y>1. Therefore, the probability is

(pi/4 - 1/2)/(1/2) = pi/2 - 1

Edited on October 25, 2017, 1:46 pm
  Posted by chun on 2017-10-25 13:24:12

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