02 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 side lengths 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 side lengths 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

How do you find the length of the hypotenuse in a 45-45-90 triangle if one leg is 8?

Back

The hypotenuse is 8√2.

Front

What is the value of x in a 30-60-90 triangle if the longer leg is 12?

Back

The shorter leg is 12/√3, and the hypotenuse is 24.

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

If x = 6 in a 30-60-90 triangle, what is the length of the hypotenuse?

Back

The hypotenuse is 12.