30-60-90 triangle calculator
Find the longer leg, hypotenuse and area of a 30°–60°–90° triangle from its shortest side.
Formula
Long leg = s√3; hypotenuse = 2s; area = s²√3/2; s in cm.
Shortest side: 3 cm · Longer leg ≈ (3 cm × 0.01 m/cm)×sqrt(3)×100 · Hypotenuse ≈ 2×(3 cm × 0.01 m/cm)×100 · Area ≈ (3 cm × 0.01 m/cm)^2×sqrt(3)÷2×10000
How to use
- Enter the shortest side opposite 30°.
- Choose its length unit.
- Read the sides in cm and area in cm².
Examples
- A 2 cm short leg gives a 4 cm hypotenuse.
Frequently asked questions
Which side do I enter?
The shorter leg, opposite the 30° angle.
What is the side ratio?
Short leg : long leg : hypotenuse = 1 : √3 : 2.
Does this work for any right triangle?
Only one with acute angles of 30° and 60°.
Sources
Updated: