Special Right Triangles

Front

What is a 30-60-90 triangle?

Back

A special right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. The sides are in the ratio 1:√3:2.

Front

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

Back

Divide the length of the long leg by √3.

Front

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

Back

Divide the length of the long leg by √3, then multiply that answer by 2.

Front

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

Back

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

Front

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

Back

Multiply the length of one leg by √2.

Front

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

Back

1 (short leg) : √3 (long leg) : 2 (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.

Front

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

Back

5.

Front

What are the side lengths of a 45-45-90 triangle if one leg is 5?

Back

Each leg is 5, and the hypotenuse is 5√2.

Front

How do you find the lengths of x and y in a 30-60-90 triangle?

Back

x = short leg, y = long leg = x√3.