Guide to the 30-60-90 Triangle

[nishamehta]

Explain 30-60-90 Triangle

 

[danisjohn]

A 30-60-90 triangle has side ratios 1:√3:2. If the shortest side is 5 (opposite 30°), the longer leg (opposite 60°) is 5√3, and the hypotenuse is 10. Example: In an equilateral triangle split in half, each half is a 30-60-90 triangle.

 

[Thornelex]

A 30-60-90 triangle is a special right triangle with angles of 30°, 60°, and 90°. The side opposite 30° is the shortest (let’s call it x), the side opposite 60° is x√3, and the hypotenuse (opposite 90°) is 2x. This ratio makes calculating missing sides very easy when you know one side.