Model a practical right triangle
Choose the endpoints and identify perpendicular separations. The direct distance is the hypotenuse; a horizontal or vertical separation is a shorter side
- Use differences Subtract coordinates or heights measured from the same reference
- Choose addition or subtraction Add squares for the direct distance; subtract a known separation square when the direct distance is given
- State the model Check perpendicular directions, level ground, straight connections and consistent units
- Report appropriately Keep intermediate values exact and state when measurements make the result an estimate
Worked example
Two vertical posts on level ground are 15 m apart and have heights 11 m and 3 m. Find the straight distance between their tops
- \(\displaystyle \Delta h=11-3=8\text{ m}\)Use the difference between the endpoint heights
- \(\displaystyle d^2=225+64=289\)The horizontal and vertical separations are perpendicular
- \(\displaystyle d=17\text{ m}\)Take the positive root. This is the straight-line model, before any fixing allowance or sag
Common mistakes
Difficulty levels
Questions about this topic
Does a turn guarantee a right angle?+
No. You need perpendicular directions or an explicit right angle. A bend in a route is not enough
Why subtract coordinates?+
Pythagoras uses the horizontal and vertical separations between the endpoints, not their positions relative to the origin
Can a real cable need more length?+
Yes. Sag, fixings, measurement uncertainty and installation requirements are outside a simple straight-line model
How do I find the hypotenuse?+
Find the right angle. The side opposite it is the hypotenuse, whatever way the triangle is drawn
When do I subtract?+
Subtract when the hypotenuse is known and a shorter side is missing. Subtract the square of the known shorter side from the square of the hypotenuse
When should I round?+
Round the final length only when requested. Keep the exact square root until that step
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 10 Mathematics, chapter 9: Pythagoras and trigonometry