Numbers x and y are chosen independently and uniformly at random from

We need the obtuse triangle whose sides are x,y and 1
As x and y lies in the interval of [0,1], the longest side of triangle must be 1
x^2 + y^2 < 1 {inequality holds for obtuse triangles)
Also we know that sum of two sides of triangle must be greater than the third side
x+y>1

We can use geometric probability to get our desired results.

Desired area is the area lie between two curves x^2 + y^2 < 1(circle of radius 1) and x+y>1(straight line)
Total area= square of side length 1

As we can see in the figure, Desired area(red portion)= {1/4(pi*1^2)}-(1/2*1*1)=pi/4-1/2
Total area= 1*1=1
The probability that x, y, and 1 are the side lengths of an obtuse triangle= (pi/4-1/2)/1=(pi/4-1/2)