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 side opposite the 30° angle.

Front

Find x in a 30°-60°-90° triangle if the shorter leg is 5.

Back

x = 5√3 (the longer leg).

Front

Find x in a 45°-45°-90° triangle if one leg is 10.

Back

x = 10√2 (the hypotenuse).

Front

What is the relationship between the sides of 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 sides of 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

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

Back

5 (the shorter leg is half the hypotenuse).

Front

If the hypotenuse of a 45°-45°-90° triangle is 14.14, what is the length of each leg?

Back

10 (each leg is 14.14/√2).

Front

Find x in a 30°-60°-90° triangle if the longer leg is 10√3.

Back

x = 10 (the shorter leg).

Front

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

Back

45°, 45°, and 90°.