Formula sheet
Pythagoras theorem
c² = a² + b² is printed on the exam formula sheet, so you do not memorise it. You must still know it works only in a right-angled triangle, and that c is always the side opposite the right angle.
What the symbols mean
- c Hypotenuse, the longest side, opposite the right angle (length unit, e.g. cm, m).
- a, b The two shorter sides (legs) that meet to form the right angle.
Given in the exam, or memorise?
c² = a² + b² is printed on the exam formula sheet, so you do not memorise it. You must still know it works only in a right-angled triangle, and that c is always the side opposite the right angle.
Why it works
It links the three sides of any right-angled triangle.
- Draw a square on each of the three sides.
- The square built on the hypotenuse has an area equal to the two smaller squares added together.
- Writing areas as side², this becomes c² = a² + b².
Worked example 1
A right-angled triangle has legs 6 cm and 8 cm. Find the hypotenuse.
- c² = a² + b² (a and b are the two legs)
- c² = 6² + 8² = 36 + 64
- c² = 100
- c = √100 = 10
Worked example 2
A right-angled triangle has hypotenuse 13 cm and one leg 5 cm. Find the other leg.
- c² = a² + b², with c = 13 and a = 5
- 13² = 5² + b²
- 169 = 25 + b²
- b² = 169 − 25 = 144
- b = √144 = 12
Where students go wrong
- Using it on a triangle that has no right angle, the theorem then gives a wrong answer.
- Putting a leg in place of c: c must be the side opposite the right angle (the longest side).
- Forgetting the final square root, so you leave the answer as c² instead of c.
- Adding the sides (a + b) instead of adding their squares (a² + b²).
Use it with
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
Is the Pythagoras theorem given in the SPM formula sheet?
Yes. c² = a² + b² is printed on the SPM Mathematics formula sheet, so you do not memorise it.
What you must know is when it applies: only in a right-angled triangle. You also need to identify c as the side opposite the right angle before you substitute the numbers.
How do I know which side is c?
c is always the hypotenuse, the longest side, lying directly opposite the right angle. The two sides that meet to form the right angle are a and b, and their order does not matter.
Find the right angle first, then the side facing it; that keeps you from mixing them up.
Can I use Pythagoras on any triangle?
No. The theorem holds only for right-angled triangles.
If the triangle has no 90° angle, c² = a² + b² gives a wrong result. Non-right triangles need other rules that lie outside this formula.
Always look for the small right-angle mark before you apply it.