Task of the Week: GeomeTREE
Our new Task of the Week is presented by Marius Moldovan. The upper secondary student from Bad Neustadt has created three math trails in Bad Neustadt together with 13 other learners as part of his school lessons. We talk about his task “GeomeTREE” task in the following interview:
How do you use MCM?
I am a student at the Rhön Gymnasium in Bad Neustadt. As part of a project in school, we (14 students) created three trails in Bad Neustadt. We have been working on the trails for several months and would like to publish them now.
Note: In the meantime two of the trails have been published:
Describe your task. How can it be solved?
My task is about determining the height of a tree. For this you should use the ray theorem or the Förster triangle. It is a good idea to form a ray set figure with the tree using a geo triangle. To do this, hold one corner of the triangle in front of your eye. One of the short sides of the triangle must be parallel to the ground, while the long side must point to the face. Then you have to decrease or increase your distance to the tree until the extension of the long side of the triangle ends exactly at the highest point of the tree. Now all you have to do is measure the distance from your point of view to the tree and add your height up to your eyes. Since the two short sides of the geo triangle are the same length, the distance to the tree is also the height of the tree from eye level.
What can you learn by working on this task?
The goal of the task is to expand students’ geometric understanding. The ray theorem should be conveyed in the task in a comprehensible way, which additionally demonstrates its possible applications outside the classroom.