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 easy calculation of side lengths. The two main types are 30°-60°-90° and 45°-45°-90° triangles.

Front

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

Back

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

Front

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

Back

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

Front

What is the length of the hypotenuse in a 30°-60°-90° triangle if the short leg is 5?

Back

The hypotenuse is 10.

Front

What is the length of the long leg in a 30°-60°-90° triangle if the short leg is 5?

Back

The long leg is 5√3.

Front

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

Back

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

Front

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

Back

In a 45°-45°-90° triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

If one leg of a 45°-45°-90° triangle is 7, what is the length of the hypotenuse?

Back

The hypotenuse is 7√2.

Front

If the hypotenuse of a 45°-45°-90° triangle is 10√2, what is the length of each leg?

Back

Each leg is 10.

Front

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

Back

It is a 30°-60°-90° triangle.