Special Right Triangles

Front

What is a 45°-45°-90° triangle?

Back

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

Front

What is a 30°-60°-90° triangle?

Back

A special right triangle where the angles are 30°, 60°, and 90°. The side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is √3 times the length of the shorter leg.

Front

If the legs of a 45°-45°-90° triangle are each 4, what is the length of the hypotenuse?

Back

4√2

Front

In a 30°-60°-90° triangle, if the shorter leg is 5, what is the length of the longer leg?

Back

5√3

Front

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

Back

The legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

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

Back

The side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is √3 times the shorter leg.

Front

Find the hypotenuse of a 45°-45°-90° triangle with legs of length 8.

Back

8√2

Front

Find the length of the shorter leg in a 30°-60°-90° triangle if the hypotenuse is 12.

Back

6

Front

What is the formula to find the hypotenuse in a 30°-60°-90° triangle?

Back

Hypotenuse = 2 * (shorter leg) or Hypotenuse = (longer leg) / √3.

Front

If the hypotenuse of a 30°-60°-90° triangle is 10, what is the length of the shorter leg?

Back

5