Special Right Triangles

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures and side length ratios, commonly the 30-60-90 triangle and the 45-45-90 triangle.

Front

What are the side ratios of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the side lengths are in the ratio 1 : √3 : 2, where 1 is the length of the short leg, √3 is the length of the long leg, and 2 is the length of the hypotenuse.

Front

What are the side ratios of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the side lengths are in the ratio 1 : 1 : √2, where the legs are equal and the hypotenuse is √2 times the length of each leg.

Front

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

Back

Multiply 4 by √3 to get the long leg, which is 4√3.

Front

If the legs of a 45-45-90 triangle are each 5, what is the length of the hypotenuse?

Back

The hypotenuse is 5√2.

Front

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

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 you know the short leg?

Back

Multiply the length of the short leg by √3.

Front

What is the length of the hypotenuse in a 45-45-90 triangle with legs of length 6?

Back

The hypotenuse is 6√2.

Front

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

Back

The short leg is 10/2 = 5.

Front

In a 30-60-90 triangle, if the long leg is 6√3, what is the length of the hypotenuse?

Back

The hypotenuse is 2 * 6√3/√3 = 12.