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 easier calculations of side lengths. The two main types are the 45°-45°-90° triangle and the 30°-60°-90° triangle.

Front

What are the angle measures of a 45°-45°-90° triangle?

Back

The angle measures are 45°, 45°, and 90°.

Front

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

Back

The ratio of the sides is 1:1:√2, where the legs are equal and the hypotenuse is √2 times the length of each leg.

Front

What are the angle measures of a 30°-60°-90° triangle?

Back

The angle measures are 30°, 60°, and 90°.

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 the side opposite the 30° angle is 1, the side opposite the 60° angle is √3, and the hypotenuse is 2.

Front

If one leg of a 45°-45°-90° triangle is 5, what is the length of the hypotenuse?

Back

The hypotenuse is 5√2.

Front

If the hypotenuse of a 30°-60°-90° triangle is 10, what is the length of the side opposite the 30° angle?

Back

The length of the side opposite the 30° angle is 5.

Front

What type of triangle is formed by angles 45°, 45°, and 90°?

Back

It is a 45°-45°-90° triangle.

Front

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

Back

It is a 30°-60°-90° triangle.

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.