GEO 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

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

Back

The hypotenuse is twice the length of the shorter leg.

Front

What is the formula for finding the length of the longer leg in a 30-60-90 triangle?

Back

The longer leg is equal to the shorter leg multiplied by √3.

Front

What is the formula for finding the length of the legs in a 45-45-90 triangle?

Back

Both legs are equal in length, and the hypotenuse is equal to the leg length multiplied by √2.

Front

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

Back

The hypotenuse is 6.

Front

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

Back

Each leg is 4√2.

Front

What is the relationship between the angles and sides in a 30-60-90 triangle?

Back

The side opposite the 30° angle is the shortest, the side opposite the 60° angle is longer, and the hypotenuse is the longest.

Front

What is the relationship between the angles and sides in a 45-45-90 triangle?

Back

Both legs are equal, and the hypotenuse is longer by a factor of √2.

Front

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

Back

Divide the length of the longer leg by √3.