20.1 Pythagoras' theorem — Practise with help
Try each problem first. Open a hint if you need it, then use the working to check your method.
Warm-up: remember
Answer these from memory. Do not look back at the section.
- Work out .
- Work out .
Answers
- . 2. .
If an answer differs, revisit Section 3.1 for squares and Section 3.2 for square roots.
Practise with help
1. Find the hypotenuse for shorter sides 3 and 4.
Hint
Square both shorter sides and add.
Full working
c² = 3² + 4² = 25, so c = 5.
2. Find the missing leg when hypotenuse is 10 and other leg is 6.
Hint
The hypotenuse square is the total.
Full working
x² = 10² − 6² = 64, so x = 8.
3. A right triangle has legs 8 and 15. Find its hypotenuse.
Hint
Name the hypotenuse before substituting.
Full working
c² = 8² + 15² = 289, so c = 17.
Before opening each full working, name the method and explain which measurements led you to choose it.