#### Activity Overview

The first problem in this activity has students explore the varying length of the third side of a triangle when 2 sides are given. They will discover that the length of the third side must be between the difference and the sum of the other 2 sides.

The second problem extends this idea of the length of the third side of a triangle to the law of cosines by plotting various lengths of the third side and fitting a curve to the data.

#### Before the Activity

The .tns file contains 2 problems. The first problem is for the Geometry student and will take approximately 1 hour. The second problem is an extension to the Pre-Calculus concept of the Law of Cosines which will take approximately 15 minutes.

#### During the Activity

The students will create triangles of varying sizes and use the data capture feature of the Nspire to record the lengths of the third side of a triangle where the other 2 sides are known. Using this data the students will discover the relationship that the length of the third side of a triangle must be between the sum of the other two sides and the difference of the other two sides.

There are some practice problems included as well.

#### After the Activity

Further explanation may be needed after the extension problem to help the students see the connection that the length of the 3rd side of a triangle is sqrt(a^2+b^2) if the angle opposite the third side is a right angle, but that length will vary by the relationship of sqrt(a^2+b^2 - 2ab*cosC) depending on the measure of angle C.