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 the hypotenuse in a 45-45-90 triangle?

Back

The length of the hypotenuse is √2 times the length of each leg.

Front

If one leg of a 45-45-90 triangle is 4, what is the length of the hypotenuse?

Back

4√2.

Front

What is a 30-60-90 triangle?

Back

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

Front

What is the relationship between the short leg, long leg, and hypotenuse in a 30-60-90 triangle?

Back

The short leg is x, the long leg is x√3, and the hypotenuse is 2x.

Front

If the short leg of a 30-60-90 triangle is 5, what is the length of the long leg?

Back

5√3.

Front

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

Back

5.

Front

How do you find the length of the other leg in a 45-45-90 triangle if one leg is known?

Back

Use the same length for the second leg.

Front

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

Back

Multiply the short leg by √3.

Front

In a 30-60-90 triangle, if the long leg is 8√3, what is the length of the short leg?

Back

8.