#### Activity Overview

A triangle is formed such that two vertices are on the base of a unit square and the third vertex somewhere within the square. What is the probability that the angle at this third vertex will be greater than 90 degrees? A diagram helps to provide a visual, the interactive nature of the TI-nspire file makes it easy for students to explore, estimate the probability and determine a geometrical approach to solving the problem.

#### Objectives

Use area and geometry to determine the probability that the angle at the vertex is greater than 90 degrees if the triangle is formed such that two vertices are on the base of a unit square and the third vertex somewhere within the unit square.

#### Vocabulary

- Area
- Sector
- Segment
- Thales law
- Vertices

#### About the Lesson

A triangle is formed such that two vertices are on the base of a unit square and the third vertex somewhere within the square. What is the probability that the angle at this third vertex will be greater than 90 degrees? What happens to the probability if a different angle is used? What is the general formula for the probability? Students use a mixture of geometry and probability to determine the answers. The interactive nature of TI-nspire helps for both the geometrical and probability approach to solving the problem.