randomly select three positive number a,b,c, and form a triangle with sides with lengths a,b,c.
what is the probabiliy that this triangle has an angle > 90 degrees?
This is a poorly-stated problem and it is not possible to solve it without additional information. The reason is that you must specify some probability distribution in order to "randomly select three positive numbers a,b,c". Do you have more information about the numbers?
(There is no probability distribution which makes all positive numbers "equally likely".)