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

Front

How do you find the length of a leg in a 45-45-90 triangle if you know the hypotenuse?

Back

Divide the length of the hypotenuse by √2.

Front

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

Back

The sides are in the ratio 1:√3:2, where 1 is the length of the shorter leg, √3 is the length of the longer leg, and 2 is the length of the hypotenuse.

Front

How do you find the length of the longer leg in a 30-60-90 triangle if you know the shorter leg?

Back

Multiply the length of the shorter leg by √3.

Front

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

Back

5 (since the shorter leg is half the hypotenuse).

Front

If the hypotenuse of a 45-45-90 triangle is 8, what is the length of each leg?

Back

Each leg is 8/√2 or 4√2.

Front

What is the length of the hypotenuse in a 30-60-90 triangle if the longer leg is 12?

Back

The hypotenuse is 12/√3 * 2 = 8√3.

Front

In a 45-45-90 triangle, if one leg is 6, what is the length of the hypotenuse?

Back

The hypotenuse is 6√2.

Front

What is the length of the longer leg in a 30-60-90 triangle if the shorter leg is 4?

Back

The longer leg is 4√3.

Front

If the hypotenuse of a 45-45-90 triangle is x, what is the formula for the length of a leg?

Back

Leg length = x/√2.