Pythagoras Theorem
Watch this video to understand how Pythagoras Theorem can be used to calculate the length of any side in a right-angled triangle.
To calculate the length of a side on a right-angled The simplest two-dimensional shape is the triangle, a three-sided shape with three angles. when you know the sizes of the other two, you need to use Pythagoras' Theorem.
Pythagoras' Theorem says that, in a right angled triangle:
The square of the The longest side of a right-angled triangle, which is opposite the right angle, is called the hypotenuse. is equal to the sum of the squares on the other two sides.
We can write this more simply as :
\({a^2} = {b^2} + {c^2}\)
Calculating the length of the hypotenuse
Question
Use Pythagoras' Theorem to calculate the length of the hypotenuse. Give your answer to 2 decimal places.
Write the equation \(x^{2} = 7^{2} + 4^{2}\)
Square the lengths you know\(x^{2} = 49 + 16\)
Add together\(x^{2} = 65\)
Find the square root\(x = \sqrt {65}\)
\(x = 8.06 (to\,2\,d.p.)\)
Question
Calculate the length of side \(x\)
(Give your answer to 2 decimal places)
\(x^{2} = 5^{2} + 9^{2}\)
\(x^{2} = 25 + 81\)
\(x^{2} = 106\)
\(x = \sqrt {106}\)
\(x = 10.30 (to\, 2\,d.p.)\)
Example
Calculate the length of the side marked \(a\).
Give your answer to 2 decimal places.
Answer
- Write the equation: \({12^2} = {a^2} + {8^2}\)
- Organise the equation \({a^2} = {12^2} - {8^2}\). To find the length of a short side, we can also use the formula \({b^2} = {a^2} - {c^2}\)
- Square the lengths you know: \({a^2} = 144 - 64\)
- Do the subtraction: \({a^2} = 80\)
- Find the square root: \(a = \sqrt {80}\)
- \(a = 8.94\,(to\,2\,d.p.)\)
Question
Calculate the length of side a.
Give your answer to 2 decimal places
\(a^{2} = 13^{2} - 9^{2}\)
\(a^{2} = 169 - 81\)
\(a^{2} = 88\)
\(a = \sqrt 88\)
\(a = 9.38\)