# Acute Triangle Probability

A random number $$\theta$$ is picked uniformly from $$(0, 180)$$. Then, a random number $$\phi$$ is picked uniformly from $$( 0 , 180 - \theta )$$. Consider the triangle which has $$\theta$$ and $$\phi$$ as two of its angles. To the nearest tenth of a percent, what is the probability that this triangle is acute?

Details and Assumptions: If your answer is 12.3%, write 12.3 in the box.

×