Pythagoras theorem formula: a² + b² = c²
The Pythagoras theorem formula is a² + b² = c².
What each letter means
- \(c\) the hypotenuse: the longest side, opposite the right angle
- \(a,\ b\) the two shorter sides
When to use it
In any right-angled triangle when you know two sides and want the third. It also gives distances between points and diagonals of boxes.
Worked example
A cuboid measures 3 cm by 4 cm by 12 cm. Find the length of its longest diagonal.
- Diagonal of the base: \(\sqrt{3^2+4^2}=5\)
- Space diagonal: \(\sqrt{5^2+12^2}=\sqrt{169}\)
Answer: 13 cm
Common mistake
Adding when you want a shorter side. To find a shorter side, subtract: a² = c² − b².
On your course
| Course | In the exam |
|---|---|
| AA SL | Not in the booklet: learn it |
| AI SL | Not in the booklet: learn it |
| AI HL | Not in the booklet: learn it |
From our own IB Maths formula sheets, in our words. The IB gives its booklet to schools, so we checked against our own copy: your teacher has the official one. Official: IB DP Mathematics page.
Practise and revise
- Practise AI SL right-angled trigonometry questions
- Practise AA SL geometry and right-angled trigonometry questions
- Revise 3D trigonometry (AI SL)
- Revise 3D geometry (AI SL)
- Print AA SL one-page formula sheet
Questions
What is the Pythagoras theorem formula?
The Pythagoras theorem formula is a² + b² = c². c: the hypotenuse: the longest side, opposite the right angle; a, b: the two shorter sides.
Is the Pythagoras' theorem given in the exam?
AA SL: not in the booklet: learn it. AI SL: not in the booklet: learn it. AI HL: not in the booklet: learn it. This comes from our own IB Maths formula sheets; your teacher has the official booklet.
How do I know which side is the hypotenuse?
It is the longest side, and it is always opposite the right angle.
Our own wording, examples and card, checked by IB Math Revision. Not produced or endorsed by the International Baccalaureate Organization.