Maths for electricians · Topic 4 of 6

Pythagoras' theorem

About 3 minutes · Diagrams, worked examples and a mini test

Pythagoras' theorem finds the third side of any right-angled triangle when you know the other two. Electricians use it for ladders, diagonal runs and, at Level 3, the power triangle.

• P – Power

The rule

c² = a² + b²

The hypotenuse c is the longest side, opposite the right angle. To find it, square the other two sides, add them, then square-root:

c = √(a² + b²)

To find a shorter side, subtract instead: a = √(c² − b²).

Worked examples

• Diagonal cable run: across a ceiling 3 m one way and 4 m the other is √(9 + 16) = √25 = 5 m.
• Ladder: to reach 8 m up a wall using the 1-in-4 rule, the foot is 2 m out. The ladder needs to be √(64 + 4) = √68 = 8.25 m long, plus about 1 m above the landing point.
• Missing side: a 10 m hypotenuse with one side of 6 m: √(100 − 36) = √64 = 8 m.

The power triangle (Level 3 preview)

In AC circuits with motors, true power P (kW) and reactive power Q (kVAr) make a right-angled triangle with apparent power S (kVA) as the hypotenuse. So S = √(P² + Q²): 3 kW and 4 kVAr give 5 kVA.

Exam tip: 3, 4, 5 is the easiest right-angled triangle to remember, and so are its multiples, like 6, 8, 10. Exam questions often use them.