30-60-90 Triangle Calculator
Sides are always in the ratio 1 : √3 : 2.
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Enter a side length and click calculate.
About 30-60-90 triangles
A 30-60-90 triangle is a special right triangle where the angles are 30°, 60°, and 90°. The sides are always in the ratio 1 : √3 : 2 — the side opposite the 30° angle is the shortest, opposite 60° is √3 times that, and the hypotenuse is twice the shortest side.
Frequently Asked Questions
What makes a 30-60-90 triangle special?▾
Its sides are always in the exact ratio 1 : √3 : 2, regardless of size. This makes its trig values (and any algebra involving them) very clean.
How is it formed?▾
Cut an equilateral triangle in half along an altitude. Each half is a 30-60-90 triangle.
Which side is opposite the 30° angle?▾
The shortest side. The side opposite 60° is √3 times longer, and the hypotenuse (opposite 90°) is twice the shortest side.
What are the trig values?▾
sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3. sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3.