2021 JMC 10 Problems/Problem 13
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Problem
An angle chosen from and an angle chosen from
determine two angles of a triangle. What is the probability this triangle is obtuse?
Solution
Let be the angle chosen from
and
be the angle chosen from
For the triangle to be obtuse, we must have
Suppose Then,
can equal
We can see that there are
desired cases and
total cases, so the answer is