Water gutter
A water gutter with optimal capacity shall be constructed from three boards with width 0.5 m each (see illustration). Show: The area of the cross section is given by the function A with
                         A(\alpha) = 0,25 \times (1 + \cos(\alpha)) \times \sin(\alpha).
Find the angle \alpha so that the water gutter has maximal capacity.
Water gutterWater gutter
The idea
A geometrical problem is described and solved algebraically by using basic geometrical formulae, functional knowledge or commands about how to find an optimal value. The technology enables a dynamic visualization of the situation to lead to a deeper understanding and an idea of solution to the optimization problem on a low level - so that you only need dynamic visualization to get an idea of the situation and a possible solution.
Aims

Detailed explanation of the aims ...
Prerequisites
CLASSROOM ACTIVITIES
Here are some hints on how to organize the work in the classroom.
letīs solve the task

all resources
Draw a sketch!
Solve the task geometrically
Solve the task algebraically!
Paper version - Word file
Short Long
Paper version - PDF
Short Long