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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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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.

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Frequently asked questions

Are answers decimals?

No, they are exact — for example 6√3.

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