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What is the 30° 60° 90° Triangle?

A 30° 60° 90° triangle is a special type of right triangle that has a 30-degree angle and a 60-degree angle in addition to the right angle.

What is the Formulas of triangle with angle 30° 60° 90° ?

1. Area = 1/2 · a · b

2. Perimeter = a + b + c

If we know the shorter leg length a, we can find out that:

3. b = √3 · a

4. c = 2a

If the longer leg length b is the one parameter given, then:

5. a = √3 / 3 · b

6. c = 2√3 / 3 · b

For hypotenuse c known, the legs formulas look as follows:

7. a = 1/2 · c

8. b = √3 / 2 · c

Where

   a：short side

   b：long side

   c：hypotenus

What is the Properties of a triangle with angle 30° 60° 90° ?

The sides of a 30° 60° 90° triangle are identified by their relation to the angles.

The side opposite the 30° is called the shorter leg.

The side opposite the 60° is called the longer leg.

The side opposite the right angle of 90° is called the hypotenuse.

It is possible to find the length of two sides of a 30° 60° 90° triangle if one side is known. The 30° 60° 90° triangle ratio for the length of the sides is as follows.

The hypotenuse is twice the shorter leg.

The longer leg is √3 times the shorter side.

If the shorter leg is a, then the hypotenuse is 2*a and the longer side is √3·a.

If the length of the shorter leg is given, then these properties are used to find the longer side and the hypotenuse. However, the 30° 60° 90° properties hold no matter which side is provided.

If the length of the hypotenuse is given, divide it by 2 for the shorter leg. Then multiply that result by √3 to get the length of the longer leg.

If the length of the longer leg is given, divide it by √3 to get the shorter leg. Then, multiply that result by two to get the length of the hypotenuse.

Using the 30° 60° 90° triangle rules, it is possible to find the lengths of the other two sides of the triangle when given the length of any one side.