Special Right Triangles 45-45-90 and 30-60-90

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are 45°, 45°, and 90°. The legs are of equal length, 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 lengths of the sides are in the ratio 1:√3:2.

Front

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

Back

The longer leg is x√3.

Front

In a 30-60-90 triangle, if the length of the hypotenuse is 'h', what is the length of the shorter leg?

Back

The shorter leg is h/2.

Front

In a 45-45-90 triangle, if the length of one leg is 'a', what is the length of the hypotenuse?

Back

The hypotenuse is a√2.

Front

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

Back

The side opposite the 30° angle is the shortest, the side opposite the 60° angle is √3 times the shortest, and the hypotenuse is twice the shortest side.

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

If the longer leg of a 30-60-90 triangle is 12, what is the length of the shorter leg?

Back

The shorter leg is 12/√3 or 4√3.

Front

What is the formula to find the hypotenuse in a 30-60-90 triangle if the shorter leg is known?

Back

Hypotenuse = 2 * (shorter leg).

Front

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

Back

Longer leg = shorter leg * √3.