### Pythagorean Triples

How many right-angled triangles are there with sides that are all integers less than 100 units?

### Tennis

A tennis ball is served from directly above the baseline (assume the ball travels in a straight line). What is the minimum height that the ball can be hit at to ensure it lands in the service area?

### Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

# Where Is the Dot?

##### Stage: 3 Challenge Level:

This problem offers students an opportunity to apply Pythagoras' Theorem.

It can also be used as a starting point for trigonometry:
• what happens to the height of the dot during the first $90^{\circ}$ of turn?
• what happens to the height of the dot when it turns beyond $90^{\circ}$?
• what can you say about the horizontal displacement of the dot as it turns through a full circle?