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

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

Back

In a 45°-45°-90° triangle, if each leg is of length 'a', then the hypotenuse is 'a√2'.

Front

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

Back

In a 30°-60°-90° triangle, if the shorter leg (opposite the 30° angle) is 'a', then the longer leg (opposite the 60° angle) is 'a√3' and the hypotenuse is '2a'.

Front

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

Back

The hypotenuse is 4√2.

Front

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

Back

The longer leg is 5√3.

Front

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

Back

Hypotenuse = 2 * (shorter leg).

Front

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

Back

Longer leg = shorter leg * √3.

Front

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

Back

The shorter leg is 5.

Front

In a 45°-45°-90° triangle, if the hypotenuse is 8√2, what is the length of each leg?

Back

Each leg is 8.