1. What is Pythagoras Theorem
Pythagoras theorem states that the square of the Hypotenuse is equal to the sum of the squares of the other two sides.
If the sides of the right-angled triangle are labelled a, b and c then Pythagoras' theorem states : a² + b² = c²
In the above diagram, side c is known as the hypotenuse, the longest side of a right-angled triangle and is opposite the right angle. Side “a” and side “b” are known as the adjacent sides.
Note: The hypotenuse is always the longest side of the right angled triangle.
If any two sides of a right angled triangle are known, one can use Pythagoras theorem to work out the length of the third side.
1.1 How to use Pythagoras Theorem
In order to use Pythagoras theorem, first label the sides of the triangle. Next write down the formula and apply the numbers and finally work out the answer.
In order to use Pythagoras theorem to find hypotenuse for the given triangle:
First label sides as a = 7 cm, b = 24 cm, c = c
It is very important to label the hypotenuse correctly with c. The adjacent sides, next to the right angle can be labelled a and b according to the size.
Next write down the formula a² + b² = c²
Apply the numbers and finally work out the answer:
Make sure you give your final answer in the correct form including units where appropriate.
1.2 Example Questions on Pythagoras theorem
Example 1: On finding the length of the hypotenuse
Find x and give your answer to 4 significant figures:
Solution:
Example 2: on finding an adjacent side.
Find x in the given triangle.
Solution:
Example 3:
Find x in the given triangle.
Solution:
