Pythagoras

Pythagoras

GCSE(F), GCSE(H),

Pythagoras` Theorem states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares on the other two sides.

Measure the length of each side, and then square the measurement. Add the squares of the two shorter sides together, and this will equal the square of the longest side.

This is written as `a^2 + b^2 = c^2`, where c is the longest side, or hypotenuse. It does not matter which sides a and b represent.

Examples

1. What is the length of the side c in this triangle? Give your answer to 1 decimal place.

Answer: 14.9 cm

Using Pythagoras` Theorem, with the shorter sides being 5 cm and 14 cm:

`a^2 + b^2 = c^2`

`5^2 + 14^2 = c^2`

`25 + 196 = c^2`

`221 = c^2`

14.866 = c, which is 14.9 to 1dp

2. What is the length of the side CB in the triangle, below? give your answer to three significant figures.

Answer: 9.59 cm

Using Pythogoras` Theorem; with the hypotenuse (c) and one shorter side known:

`a^2 + b^2 = c^2`

`22^2 + b^2 = 24^2`

`484 + b^2 = 576`

Rearranging the equation:

`b^2 = 576 - 484`

`b^2 = 92`

b = 9.59166`, or 9.59 to 3sf