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.