Late at night, young Pythagoras tries to climb his 5 m long ladder up to his darling's window. The window is 4.50 m above the ground.

(1) How high will he get if he places the ladder 3 m off the wall? In the drawing above, drag the point on the ground and find the solution. Sketch the solution with all its lengths (s, r, h) on paper.
(2) Now, try to calculate the solution of task (1) on paper. Which lengths are given, which are sought? Do you get the same solution as in (1)?
(3) At what distance of the wall should Pythagoras place his ladder in order to reach the window 4.50 meters above the ground? Find the solution again by dragging the point on the ground. Sketch the solution with all its lengths (s, r, h) on paper.
(4) Now, try to calculate the solution of task (3) on paper. Which lengths are given, which are sought? Does your solution accord to your sketch made in (3)?