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

Back

In a 45-45-90 triangle, the sides are in the ratio 1:1:√2.

Front

What are the side ratios of 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 x, what is the length of the hypotenuse?

Back

The hypotenuse is x√2.

Front

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

Back

The longer leg is x√3.

Front

If the hypotenuse of a 30-60-90 triangle is 2x, what is the length of the shorter leg?

Back

The shorter leg is x.

Front

What is the length of the hypotenuse in a 45-45-90 triangle if each leg is 4?

Back

The hypotenuse is 4√2.

Front

What is the length of the longer leg in a 30-60-90 triangle if the shorter leg is 5?

Back

The longer leg is 5√3.

Front

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

Back

Each leg is 10.

Front

In a 30-60-90 triangle, if the hypotenuse is 12, what is the length of the shorter leg?

Back

The shorter leg is 6.