Pythagoras Theorem

Pythagoras Theorem is a method used to work out the length of the side of a triangle providing

a. the triangle is right-angled.

b. The lengths of the other two sides are known

An example of this is shown above.

 The longest side of a right-angled triangle is called the hypotenuse

And Pythagoras Theorem is

a and b are the lengths of the shorter sides, so for this triangle

So for this triangle the length of the hypotenuse squared is 25.

So the length of the hypotenuse,

 

For most triangles, the length of at least one of its sides is not a whole number.

Now 58 is not a square number and so to find its square root a calculator is needed.

But 58 is between the square numbers 49 and 64, so Ö 58 is between Ö 49 and Ö 64,

that is Ö 58 is between 7 and 8. So the solution can be finished with

The symbol means "is approximately".

Find the length of the hypotenuse of each of these triangles. If necessary use the table at the right to work out the approximate answers.

x

1

4

9

16

25

36

49

64

81

100

121

144

169

196

225

256

289

324

361

400

Ö x

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Pythagoras theorem can still be used when working out the length of one of the shorter sides from the hypotenuse and the other side, as long as you are careful to put the right numbers into the right places in the formula.

Now try these.

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