Special Right Triangles Calculator

Find all sides of a 45-45-90 or 30-60-90 triangle from the short side.

Second side 6.928

Hypotenuse 8

Formula: 45-45-90: s, s, s√2 · 30-60-90: s, s√3, 2s

Step-by-step with your numbers:

1. Values used:

2. Short side = 4

4. Second side = 6.928

5. Hypotenuse = 8

Did we solve your problem today?

Special right triangles have fixed side ratios, so one side gives you them all.

The math behind it

A 45-45-90 triangle has sides in ratio 1 : 1 : √2. A 30-60-90 triangle has ratio 1 : √3 : 2 (short : long : hypotenuse).

30-60-90 with short side 4 → long 6.93, hypotenuse 8.

Which side is 'short'?

The side opposite the smallest angle (30° or one of the 45°s).