Pythagoras Theorem

-


Quiz 1




Pythagoras Theorem: Complete Theory and Formulas

Fundamental Theorem

In any right-angled triangle:

a² + b² = c²

Where:
- a, b = legs (shorter sides)
- c = hypotenuse (longest side)

Right triangle diagram

Derived Formulas

Find hypotenuse (c):

c = √(a² + b²)

Find leg (a):

a = √(c² - b²)

Example Problems

Example 1: Find hypotenuse (c) when a=6cm, b=8cm

6² + 8² = c²
36 + 64 = 100 → c = √100 = 10cm

Example 2: Find leg (a) when b=5cm, c=12cm

a² = 12² - 5²
a² = 144 - 25 = 119 → a ≈ 10.9cm (3 s.f.)

3D Applications

Space diagonal in cuboid:

d² = l² + w² + h²

Example: For 6×5×4 cuboid:
AG = √(6² + 5² + 4²) = √77 ≈ 8.77cm

Practice Exercises

  1. Calculate diagonal of rectangle 8cm×15cm
  2. Find height of cone with slant height 10cm and radius 3cm
  3. Determine if triangle 7cm, 24cm, 25cm is right-angled