Pythagoras' theorem
In a right-angled triangle, the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides: a^2 + b^2 = c^2.
Last updated
Analogy
Like fitting square tiles onto each side: the two small squares cover exactly the big one.
Example
Short sides 5 and 1225 + 144 = 169sqrt(169) = 13To find a short side: 10^2 - 6^2 = 64, so 8
In practice
Builders check a corner is square by measuring 3, 4 and 5 along the sides.
Practice
Flashcards
- What are the short sides of a right triangle if the hypotenuse is 13 and one side is 5?12. 169 - 25 = 144, and sqrt(144) = 12.
Interview questions
- Find the length of the hypotenuse of a right-angled triangle with shorter sides 5 cm and 12 cm. Explain each step.
- Pythagoras: a^2 + b^2 = c^2
- 25 + 144 = 169
- c = sqrt(169)
- c = 13 cm
Questions people ask
Which side is the hypotenuse?
The hypotenuse is the longest side of a right-angled triangle. It is always opposite the right angle. In a^2 + b^2 = c^2, the letter c stands for the hypotenuse. The other two sides are interchangeable. Spot it first, before putting any numbers into the formula, to avoid mixing the sides up.
When do you subtract in Pythagoras?
You subtract when you are finding one of the shorter sides and you know the hypotenuse. Rearranging gives a^2 = c^2 - b^2. For a hypotenuse of 10 and a side of 6, a^2 = 100 - 36 = 64, so a = 8.