30-60-90 Triangles

Front

What is a 30-60-90 triangle?

Back

A special type of right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees.

Front

What is the ratio of the sides in a 30-60-90 triangle?

Back

The ratio of the lengths of the sides opposite the 30°, 60°, and 90° angles is 1 : √3 : 2.

Front

If the short leg of a 30-60-90 triangle is 6, what is the length of the long leg?

Back

The long leg is 6√3.

Front

If the hypotenuse of a 30-60-90 triangle is 12, what is the length of the short leg?

Back

The short leg is 6.

Front

What is the formula to find the length of the hypotenuse in a 30-60-90 triangle?

Back

Hypotenuse = 2 * (short leg).

Front

How do you find the length of the long leg in a 30-60-90 triangle?

Back

Long leg = short leg * √3.

Front

If the long leg of a 30-60-90 triangle is 12√3, what is the length of the short leg?

Back

The short leg is 12.

Front

What is the value of x in a 30-60-90 triangle if the short leg is x?

Back

The hypotenuse is 2x and the long leg is x√3.

Front

Is a triangle with sides 5, 5√3, and 10 a 30-60-90 triangle?

Back

Yes, it follows the ratio 1 : √3 : 2.

Front

What is the area of a 30-60-90 triangle with a short leg of 4?

Back

Area = (1/2) * (short leg) * (long leg) = (1/2) * 4 * (4√3) = 8√3.