Special Right Triangles

Front

What is a 30-60-90 triangle?

Back

A special right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. The sides are in the ratio 1:√3:2.

Front

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

Back

Divide the length of the long leg by √3.

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are both 45 degrees and the sides are in the ratio 1:1:√2.

Front

How do you find the length of a leg in a 45-45-90 triangle if the hypotenuse is given?

Back

Divide the length of the hypotenuse by √2.

Front

What is the relationship between the legs and the hypotenuse in a 45-45-90 triangle?

Back

The legs are equal in length, and each leg is √2 times shorter than the hypotenuse.

Front

If the hypotenuse of a 45-45-90 triangle is 8, what is the length of each leg?

Back

Each leg is 8/√2 or 4√2.

Front

If the long leg of a 30-60-90 triangle is 7, what is the length of the short leg?

Back

The short leg is 7/√3.

Front

What is the formula to find the hypotenuse in a 45-45-90 triangle?

Back

Hypotenuse = leg × √2.

Front

What is the formula to find the long leg in a 30-60-90 triangle?

Back

Long leg = short leg × √3.

Front

If the short leg of a 30-60-90 triangle is 4, what is the length of the hypotenuse?

Back

The hypotenuse is 4 × 2 = 8.