Pythagoras' theorem
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Explainer Video
Summary
Pythagoras' theorem
In a nutshell
Pythagoras' theorem is very useful when trying to find the value for the third side of a right-angled triangle. Additionally, at this level, you may have to apply the formula to finding the distance between 2 points on a graph.
Recap
Pythagoras' theorem says that:
Where and are the two shorter sides of a right-angled triangle and is the hypotenuse.
Note: Pythagoras' theorem only works for a right-angled triangle. If there is no right-angle, then you cannot use Pythagoras' theorem.
Hypotenuse
The hypotenuse of a triangle is the longest side. For a right-angled triangle, the hypotenuse is always the side opposite the right-angle.
Distance between two points on a graph
You may be asked to find the distance between 2 given coordinates. Approaching these types of problems always requires the same method.
PROCEDURE
1. | Do a quick sketch of the graph with the given coordinates and draw a right-angled triangle with the two points. |
2. | Find the lengths of the two shorter sides of the triangle. |
3. | Use Pythagoras' theorem to find the length of the hypotenuse of the triangle - this is the distance. |
Example
Find the distance between the points and .
First, make a quick sketch:
The length of the horizontal side is:
The length of the vertical side is:
The distance (labelled ) will then satisfy Pythagoras' theorem:
FAQs - Frequently Asked Questions
How do I find the distance between 2 points on a graph?
First sketch the graph and points. Then, make a right-angled triangle with the points and use Pythagoras' Theorem.
What is the hypotenuse of a triangle?
The hypotenuse of a triangle is the longest side.
When can I use Pythagoras' Theorem?
You can only use Pythagoras' Theorem when you are given 2 sides of a right-angled triangle and want to find the third side.