Special Right Triangles

Front

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

Back

In a 30-60-90 triangle, the sides are in the ratio 1 : √3 : 2, where 1 is the length of the short leg, √3 is the length of the long leg, and 2 is the length of the hypotenuse.

Front

How do you find the hypotenuse in a 30-60-90 triangle if you are given the long leg?

Back

To find the hypotenuse, divide the length of the long leg by √3 and then multiply by 2.

Front

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

Back

In a 45-45-90 triangle, the legs are equal in length.

Front

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

Back

To find the hypotenuse, multiply the length of a leg by √2.

Front

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

Back

To find the short leg, divide the length of the long leg by √3.

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, which simplifies to 4√2.

Front

What is the value of the short leg in a 30-60-90 triangle if the long leg is 6?

Back

The short leg is 6/√3, which simplifies to 2√3.

Front

In a 30-60-90 triangle, if the short leg is 5, what is the length of the hypotenuse?

Back

The hypotenuse is 10, since it is twice the length of the short leg.

Front

What is the length of the long leg in a 30-60-90 triangle if the short leg is 4?

Back

The long leg is 4√3.

Front

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

Back

The length of the second leg is the same as the length of the first leg.