VG1
geometri
Quiz
The Pythagorean theorem
The Pythagorean theorem is one of the most famous in mathematics, describing the relationship between the sides of a right-angled triangle.
Right-angled triangle
A right-angled triangle has a 90-degree angle. The side opposite this angle is called the hypotenuse — always the longest side. The other two sides are called legs.
The theorem
a² + b² = c²
where c is the hypotenuse and a, b are the legs.
Example 1 — find the hypotenuse
Legs a = 3, b = 4. Find c:
c² = 3² + 4² = 9 + 16 = 25
c = √25 = 5
c = √25 = 5
Example 2 — find a leg
Hypotenuse c = 13, leg a = 5. Find b:
b² = 13² - 5² = 169 - 25 = 144
b = √144 = 12
b = √144 = 12
Practical example
A house is 4 m tall and you stand 3 m from the wall. How long must the ladder be?
c² = 4² + 3² = 25 → c = 5 metres
c² = 4² + 3² = 25 → c = 5 metres
Important: This theorem only works in right-angled triangles!
Pythagorean triples
| a | b | c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
There is geometry in the humming of the strings, there is music in the spacing of the spheres.
— Pythagoras (570–495 BC)
🧠 Test yourself
Question 1 of 3
Legs 6 and 8. What is the hypotenuse?