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

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are both 45 degrees and the right angle is 90 degrees. The sides are in the ratio 1 : 1 : √2.

Front

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

Back

The long leg is x√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 12/2 = 6.

Front

How do you find the hypotenuse of a 45-45-90 triangle if one leg is 5?

Back

The hypotenuse is 5√2.

Front

What is the formula to find the length of the short leg in a 30-60-90 triangle if the long leg is known?

Back

Short leg = Long leg / √3.

Front

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

Back

Each leg is 8/√2 or 4√2.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

The sides are in the ratio 1 (short leg) : √3 (long leg) : 2 (hypotenuse).

Front

If the long leg of a 30-60-90 triangle is 9, what is the length of the hypotenuse?

Back

The hypotenuse is 9/√3 * 2 = 6√3.

Front

What is the length of the hypotenuse in a 45-45-90 triangle if one leg is 10?

Back

The hypotenuse is 10√2.