Special Right Triangles

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures that allow for simplified calculations of side lengths. The two main types are 45-45-90 and 30-60-90 triangles.

Front

What are the angles in a 45-45-90 triangle?

Back

The angles in a 45-45-90 triangle are 45 degrees, 45 degrees, and 90 degrees.

Front

What is the ratio of the sides in a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the ratio of the lengths of the legs to the hypotenuse is 1:1:√2.

Front

What are the angles in a 30-60-90 triangle?

Back

The angles in a 30-60-90 triangle are 30 degrees, 60 degrees, and 90 degrees.

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 shorter leg, longer leg, and hypotenuse is 1:√3:2.

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 10, what is the length of each leg?

Back

Each leg is 5√2.

Front

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

Back

The longer leg is 4√3.

Front

What is the length of the hypotenuse in a 30-60-90 triangle if the longer leg is 6√3?

Back

The hypotenuse is 12.

Front

What type of triangle is formed by angles of 30°, 60°, and 90°?

Back

It is a 30-60-90 triangle.