The purpose of this multi-level task is to engage students in using deductive steps, including the applications of Pythagoras' theorem to solve a problem.

The background knowledge presumed for this task is outlined in the diagram below:

This task may be carried out with numerical exploration based on scale diagram or calculation of lengths, and/or by use of right angled triangle processes that have been established earlier. The approach should be chosen in sympathy with their skills and depth of understanding.

Task: A land based windsurfer is being constructed by affixing a mast and sail to a skateboard. The sail has a bar fixed to the side of the mast and going across the sail as shown in black in the diagram.

The sail is a right angled triangle with a base of 1m and the length of the hypotenuse is 2m. The bar starts at the vertex of the sail as shown and meets the hypotenuse at right angles.

Find the length of the bar.

### The arithmetic approach (show more)

- The student is able to construct a scale diagram to solve the problem to a reasonable degree of accuracy and to use Pythagoras' theorem to verify their result.

### The procedural algebraic approach (show more)

- The student is able to solve a right angled triangle problem using trigonometric ratios and Pythagoras' theorem.

### The conceptual algebraic approach (show more)

- The student is able to solve a right angled triangle problem with the greatest possible accuracy.