Special Right Triangles

Front

What are special right triangles?

Back

Special right triangles are triangles with specific angle measures that allow for easy calculation of side lengths. The two main types are the 45°-45°-90° triangle and the 30°-60°-90° triangle.

Front

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

Back

In a 45°-45°-90° triangle, the sides are in the ratio 1:1:√2.

Front

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

Back

In a 30°-60°-90° triangle, the sides are in the ratio 1:√3:2.

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

Back

The longer leg is 4√3.

Front

What is the measure of the angles in a 45°-45°-90° triangle?

Back

The angles are 45°, 45°, and 90°.

Front

What is the measure of the angles in a 30°-60°-90° triangle?

Back

The angles are 30°, 60°, and 90°.

Front

How do you find the length of the hypotenuse in a 30°-60°-90° triangle?

Back

The hypotenuse is twice the length of the shorter leg.

Front

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

Back

Each leg is 10/√2 or 5√2.

Front

What is the relationship between the angles and sides in special right triangles?

Back

The angles determine the ratios of the sides, allowing for quick calculations.