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 the hypotenuse is known?

Back

Divide the length of the hypotenuse by √2.

Front

How do you find the hypotenuse in a 45-45-90 triangle if a leg is known?

Back

Multiply the length of the leg by √2.

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

How do you find the hypotenuse in a 30-60-90 triangle if the short leg is known?

Back

Multiply the length of the short leg by 2.

Front

How do you find the long leg in a 30-60-90 triangle if the short leg is known?

Back

Multiply the length of the short leg by √3.

Front

What is the relationship between the legs in a 45-45-90 triangle?

Back

The legs are equal in length.

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

In a 30-60-90 triangle, if the long leg is 4√3, what is the length of the short leg?

Back

The short leg is 4.

Front

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

Back

The hypotenuse is the long leg divided by √3.