Task of the Week: Illumination of the Castle Garden

This week the “Task of the Week” focuses on a typical application of the intercept theorems. In particular, it is about the height determination of objects using the interception theorems. This task type can be transferred to many different objects and can therefore be found in further MathCityMap trails. The here described example is about the height determination of the lanterns in the garden of Erlangen’s castle.

Task: Illumination of the Castle Garden (task number: 709)

Determine the height of the two-armed lamps in the castle garden in the unit cm.

To solve the problem, the second intercept theorem is required. For this purpose, the pupils position themselves a few meters away from the object and fix the object. The intercept theorem can then be applied using the measuring stick. For this, the eye height as well as the distance to the object must be measured. With the arm outstretched, the measuring stick is held so that its tip coincides with the upper end of the lantern. The length of the arm and the scale length, which corresponds to the height of the lantern from the height of the eye, lead to the height of the lantern.

This is a problem-solving situation in which initially missing values have to be determined by a suitable initial situation. The application of the interception theorem can in this case be facilitated through the preparation of a sketch. The task is particularly suited to show students the practical application of the interception theorem and to give a meaningful content to the calculus.