Special Right Triangles

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the two legs are of equal length and the angles are 45°, 45°, and 90°.

Front

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

Back

The length of each leg is the hypotenuse divided by √2.

Front

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

Back

Divide the length of the hypotenuse by √2.

Front

What is a 30-60-90 triangle?

Back

A special right triangle with angles measuring 30°, 60°, and 90°.

Front

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

Back

The length of the short leg is half the hypotenuse, and the long leg is the short leg multiplied by √3.

Front

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

Back

Divide the length of the long leg by √3.

Front

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

Back

5 (half of the hypotenuse).

Front

If the short leg of a 30-60-90 triangle is 4, what is the length of the long leg?

Back

4√3 (short leg multiplied by √3).

Front

What are the side lengths of a 45-45-90 triangle with a hypotenuse of 8?

Back

Each leg is 8/√2 or 4√2.

Front

What are the side lengths of a 30-60-90 triangle with a hypotenuse of 12?

Back

Short leg = 6, Long leg = 6√3.