Applying Pythagoras’ theory

Task goals

• Spot the right-angled triangle hidden in a shape (rectangle diagonal, isosceles triangle height) or a real-world situation (ladder, travel path, guy-wire) before applying the theorem.
• Find a missing hypotenuse or shorter side using $a^2+b^2=c^2$, choosing addition or subtraction correctly for the context.
• Round an answer to a stated number of decimal places when the lengths are not a perfect-square triple.
• Use a Pythagoras answer as the starting point for a second calculation, such as an area, a perimeter, or a comparison between two routes.