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

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

Back

Multiply the length of a leg by √2.

Front

What is the ratio of the sides in a 45-45-90 triangle?

Back

1:1:√2, where the legs are 1 and the hypotenuse is √2.

Front

What is a 30-60-90 triangle?

Back

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

Front

How do you find the length of the hypotenuse in a 30-60-90 triangle?

Back

Multiply the length of the shorter leg (opposite the 30° angle) by 2.

Front

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

Back

1:√3:2, where the shorter leg is 1, the longer leg is √3, and the hypotenuse is 2.

Front

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

Back

4 (the legs are equal in length).

Front

If the hypotenuse of a 45-45-90 triangle is 8√2, what is the length of each leg?

Back

8 (divide the hypotenuse by √2).

Front

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

Back

5√3 (multiply the shorter leg by √3).

Front

If the longer leg of a 30-60-90 triangle is 6√3, what is the length of the shorter leg?

Back

6 (divide the longer leg by √3).