Special Right Triangles 45-45-90 and 30-60-90

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are 45°, 45°, and 90°. The legs are of equal length, and the hypotenuse is √2 times the length of a leg.

Front

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

Back

The ratio of the sides is 1 : √3 : 2, where 1 is the length of the shorter leg (opposite the 30° angle), √3 is the length of the longer leg (opposite the 60° angle), and 2 is the length of the hypotenuse.

Front

If the leg of a 45-45-90 triangle is 14, what is the length of the hypotenuse?

Back

The hypotenuse is 14√2.

Front

In a 30-60-90 triangle, if the shorter leg is 4, what is the length of the longer leg?

Back

The longer leg is 4√3.

Front

What is the length of the hypotenuse in a 30-60-90 triangle if the shorter leg is 10?

Back

The hypotenuse is 20.

Front

If the hypotenuse of a 45-45-90 triangle is 13√2, what is the length of each leg?

Back

Each leg is 13.

Front

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

Back

Multiply the length of the shorter leg by √3.

Front

What is the length of the hypotenuse in a 30-60-90 triangle if the longer leg is 10√3?

Back

The hypotenuse is 20.

Front

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

Back

Each leg is x/√2.

Front

In a 30-60-90 triangle, if the longer leg is 10, what is the length of the shorter leg?

Back

The shorter leg is 10/√3.