# Acute triangles?

- Author:
- Steve Phelps

A point P is placed randomly in the interior of equilateral triangle ABC. What is the probability that at least one of triangles PAB, PBC, or PCA is acute?

## Intuition

Do you think the probability of at least one acute triangle is greater than 0.5 or less than 0.5? Explain why you think this?

What is your best guess (what does your gut tell you?) of the probability of at least one acute triangle? Explain why you think this is a reasonable probability.

## Simulation

## Mathematics

Explain how the app below can help you compute the probability of at least one acute triangle?