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Concept

$30 - 60 - 90$ Triangle

30 - 60 - 90

triangle is a special type of right triangle. It has two acute angles measuring

3 0^{\circ}

and

6 0^{\circ}

in addition to the right angle.

A right triangle with the angles of 30, 60, and 90 degrees

If the shorter leg in a $30 - 60 - 90$ triangle has the length $ℓ,$ the longer leg will have the length $3 ℓ,$ and the length of the hypotenuse will be $2 ℓ .$

A right triangle with the angles of 30, 60, and 90 degrees and the side lengths equal l, 2l, and a square root of 3 times l

These relations can be deducted from the trigonometric ratios and the known trigonometric values of the notable angles.

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