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 that make calculations easier. The two main types are the 45-45-90 triangle and the 30-60-90 triangle.

Front

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

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of a leg.

Front

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

Back

Multiply the length of the leg by √2.

Front

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

Back

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

Front

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

Back

Multiply the length of the short leg by √3.

Front

How do you find the length of 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

If the hypotenuse of a 45-45-90 triangle is 10√2, what is the length of each leg?

Back

Each leg is 10.

Front

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

Back

The hypotenuse is 10.

Front

If the longer leg of a 30-60-90 triangle is 8√3, what is the length of the short leg?

Back

The short leg is 8.

Front

What is the formula to find the hypotenuse in a 45-45-90 triangle?

Back

Hypotenuse = leg × √2.