In a right-angled triangle, the longest side is the hypotenuse, opposite the right angle. Pythagoras' theorem says a² + b² = c², where c is the hypotenuse and a and b are the shorter sides.
To find the hypotenuse, square the two shorter sides, add, then take the square root. To find a shorter side, square the hypotenuse, subtract the square of the other side, then take the square root. Answers are often not whole numbers, so round as the question asks.
Worked example
A right-angled triangle has shorter sides of 12 cm and 3 cm. Find the hypotenuse to 1 decimal place.
- 12² + 3² = 144 + 9 = 153.
- √153 = 12.369…
Answer:12.4 cm
Key words
- hypotenuse
- the longest side, opposite the right angle
- Pythagoras' theorem
- a² + b² = c²
- square root
- undoes squaring
Practise this
New questions every time.
Common Core-referenced: 8.G.B.7