Special Right Triangles Worksheet
Find missing sides of 45-45-90 and 30-60-90 triangles using the side ratios. Answers are exact, in simplest radical form.
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- No AI — answers are calculated, not guessed
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Example worksheets
Made with this tool — click any example to see it full size.
Best for: Geometry (grades 9–10)
45-45-90
The legs are equal and the hypotenuse is a leg times √2: legs 5 and 5, hypotenuse 5√2.
30-60-90
The short leg (opposite 30°) is s, the long leg is s√3, and the hypotenuse is 2s.
Make it a timed challenge
Put a visual classroom timer on the board and see how many problems students can finish before the time runs out. Print a new version tomorrow and try to beat the score.
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Frequently asked questions
Are answers decimals?
No, they are exact — for example 6√3.
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