Measurement applications: Pythagoras

Task goals

• Apply Pythagoras' theorem to find a missing hypotenuse or a missing leg of a right-angled triangle in a real-world measurement scenario.
• Decide, from a real-world description, which of the three sides of a right-angled triangle is the hypotenuse before applying Pythagoras' theorem.
• Use a length found with Pythagoras' theorem as an input to a further perimeter, area, surface area, or volume calculation, never leaving a "missing side" answer unused.
• Convert between units of length before or after applying Pythagoras' theorem, and round an irrational answer to a stated number of decimal places without losing precision partway through a multi-step calculation.
• Use a length found with Pythagoras' theorem, a material's coverage rate or unit size, and a price to find a total quantity and cost.
• Round a discrete purchase (battens, sheets, rolls) UP to the next whole item even when only slightly over, and calculate the total cost to the nearest cent.
• Calculate the volume of material associated with a Pythagoras-derived length, such as the fill beneath a sloped structure's triangular cross-section.
• Compare two real material or supplier options by total cost and/or a non-cost factor (such as an outdoor-rating requirement), check a stated budget constraint, and write a short, numbers-based justification for a real-world measurement decision.