Pythagorean theorem examples
Use these examples to review the Pythagorean method before entering your own triangle problem in the app.
What this topic means and what to look for first.
Pythagoras applies to right-angled triangles.
The relationship is a^2 + b^2 = c^2, where c is the hypotenuse.
One reliable route through the topic.
- 1Identify the hypotenuse first.
- 2Substitute the known side lengths into a^2 + b^2 = c^2.
- 3Rearrange if you need to find a shorter side.
- 4Square root the final value carefully.
- 5Check the answer is sensible for the triangle shown.
See the method in action.
Find the hypotenuse when the shorter sides are 3 and 4.
- Use 3^2 + 4^2 = c^2.
- So 9 + 16 = 25.
- Therefore c = 5.
Find the missing shorter side when c = 13 and one side is 5.
- Use a^2 + 5^2 = 13^2.
- So a^2 + 25 = 169.
- Therefore a^2 = 144 and a = 12.
Things that commonly send the method off track.
- Using Pythagoras on a triangle that is not right-angled.
- Mixing up the hypotenuse with one of the shorter sides.
Want to test your own problem next?
Use the public page first, then create a free account if you want to try the solver beta on a typed question or photo.
A free account is the current follow-up route for returning to the solver beta and future guide updates as the public library grows.
Want to try a similar problem yourself?
Create a free account if you want to use the solver beta after reading the guide.
A free account is the current follow-up route for returning to the solver beta and future guide updates as the public library grows.
Extra geometry revision resources
These printed-resource searches are useful if you want more diagrams and geometry practice than one page can provide.
Amazon
Geometry workbook search
Useful for shape, angle, and diagram-heavy practice when you want more than a single online example set.
View Geometry workbook searchAmazon
Trigonometry revision book search
A practical follow-up if you want more triangle, sine, cosine, and tangent examples in print.
View Trigonometry revision book searchFound this useful?
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Short answers worth checking.
It is the longest side and it is opposite the right angle.
Yes. Many triangle lengths are not exact whole numbers.
Continue with the next closely related topic.
Use the public site structure first, then switch into the solver tool only if you need a direct test.
CureMath uses artificial intelligence to suggest how a maths problem could potentially be solved. AI can make mistakes.
Check important answers independently before relying on them.