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Learner Guide

Maths

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Pythagoras

L . O to find the length of an unknown side using Pythagoras

This is the method of finding the length of different sides in a right angled

triangle.Firstly, you should be comfortable with labeling the: adjacent

opposite and hypotenuse of any right angle triangle, we will cover this

more on the Trigonometry section.

All you have to do is follow one simple rule:

 a2 + b2 = c2

Let’s try an example:

Here we have a right angle triangle with side lengths of 3cm, 4cm and 5cm.

Pythagoras Theorem uses the square of the length of each side.

Now if we look at the areas of each square:

The area of the square on the side length of 3 cm is 9 cm. The area of the

square on the side length of 4 cm is 16 cm.

The area of the square on the side length of 5 cm (the hypotenuse)  is 25 cm.

Notice that using:

 a2 + b2 = c2

9 + 16 = 25 which is the same as 32 + 42 = 52

Example 1

Work out the length of the hypotenuse of this triangle. Always state

Pythagoras’ Theorem first.

82 + 152 = c2

64 + 225 = c2

c2 = 289

c = √289 = 17

The length of the hypotenuse if 17 cm.

 a2 + b2 = c2 Step 2: Substitute the given lengths. Step 3: Work out the squares. Step 4:   Don’t be caught out here, you have the c2 but to find out the length of c you have to find the square root.

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