Pythagoras' theorem
Pythagoras' theorem relates the lengths of the sides of a
right-angled triangle. This leaflet reminds you of the theorem
and provides some revision examples and exercises.
Study the right-angled triangle shown.
In any right-angled triangle, ABC , the side opposite the
right-angle is called the hypotenuse. Here we use the convention
that the side opposite angle A is labelled a. The side opposite B
is labelled b and the side opposite C is labelled c. Pythagoras'
theorem states that the square of the hypotenuse, (c ),
is equal to the sum of the squares of the other two sides, (a +
b )
Pythagoras' theorem: c =
a + b
Example
Suppose AC = 9 cm and BC = 5 cm as shown. Find the length of
the hypotenuse, AB .
Solution
Here, a = BC = 5, and b = AC = 9. Using the theorem
The hypotenuse has length 10.30cm.
Example
In triangle ABC shown, suppose that the length of the
hypotenuse is 14cm and that a = BC = 3 cm. Find the length of AC.
Solution
Here a = BC = 3, and c = AB = 14. Using the theorem
The length of AC is 13.67cm.
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