Special Right Triangles

Front

What are the two types of special right triangles?

Back

The two types of special right triangles are 45-45-90 triangles and 30-60-90 triangles.

Front

What is the relationship between the legs of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of each leg.

Front

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

Back

In a 30-60-90 triangle, the ratio of the lengths of the sides is 1 : √3 : 2, corresponding to the short leg, long leg, and hypotenuse, respectively.

Front

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

Back

The hypotenuse is 6, since it is twice the length of the short leg.

Front

How do you find the length of the hypotenuse in a 45-45-90 triangle if one leg is 4?

Back

The hypotenuse is 4√2, since it is √2 times the length of each leg.

Front

What is the length of the long leg in a 30-60-90 triangle if the short leg is 5?

Back

The long leg is 5√3, since it is √3 times the length of the short leg.

Front

What is the formula for the hypotenuse in a 30-60-90 triangle?

Back

The hypotenuse is 2 times the length of the short leg.

Front

In a 45-45-90 triangle, if the hypotenuse is 10, what is the length of each leg?

Back

Each leg is 10/√2 or 5√2.

Front

What is the length of the short leg in a 30-60-90 triangle if the hypotenuse is 12?

Back

The short leg is 6, since it is half the length of the hypotenuse.

Front

What is the length of the hypotenuse in a 30-60-90 triangle if the long leg is 8√3?

Back

The hypotenuse is 16, since the long leg is √3 times the short leg, which is 8/√3.