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 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 sides are in the ratio 1:1:√2.

Front

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

Back

In a 30-60-90 triangle, the sides are in the ratio 1:√3:2.

Front

If the legs of a 45-45-90 triangle are each 2, what is the length of the hypotenuse?

Back

The hypotenuse is 2√2.

Front

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

Back

The longer leg is 3√3.

Front

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

Back

The shorter leg is 5.

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

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

Back

Multiply the length of the shorter leg by √3.

Front

What is the length of the hypotenuse if the legs of a 45-45-90 triangle are 4?

Back

The hypotenuse is 4√2.

Front

What is the length of the hypotenuse if the shorter leg of a 30-60-90 triangle is 6?

Back

The hypotenuse is 12.