The diagram below shows a simplified side view of a garden roller. The radius of the cylinder is 30 cm. The length of the handle is 130 cm. The roller is leaning against a wall with the handle at an angle of 25 degrees to the vertical the ground is horizontal.

A gardener takes the roller on to a lawn. Just as he begins to roll he notices a small scratch at the highest point of the cylinder.

(iv) Show that, when the cylinder has been pushed a distance x cm on the lawn, the height of the scratch above the ground is:

30{1+cos(6x/pi)}cm

Anyone know how to get there?