What is a 30-60-90 triangle?

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A 30-60-90 triangle is a right triangle with three angles that measure 30 degrees, 60 degrees, and 90 degrees. It is a special type of right triangle because its sides are in a specific ratio to each other. In a 30-60-90 triangle, the length of the side opposite the 30-degree angle is half the lengtRead more

A 30-60-90 triangle is a right triangle with three angles that measure 30 degrees, 60 degrees, and 90 degrees. It is a special type of right triangle because its sides are in a specific ratio to each other.

In a 30-60-90 triangle, the length of the side opposite the 30-degree angle is half the length of the hypotenuse, and the length of the side opposite the 60-degree angle is the product of the square root of 3 and the length of the side opposite the 30-degree angle. The length of the hypotenuse is twice the length of the side opposite the 30-degree angle.

More specifically, if we let the length of the side opposite the 30-degree angle be x, then:

These ratios are always true for any 30-60-90 triangle, regardless of the size of the triangle.

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