Special Right Triangles

Front

What is a special right triangle?

Back

A triangle with one angle measuring 90 degrees and specific properties that allow for easier calculations of side lengths.

Front

What are the two types of special right triangles?

Back

45-45-90 triangle and 30-60-90 triangle.

Front

In a 45-45-90 triangle, what is the ratio of the lengths of the legs to the hypotenuse?

Back

The legs are equal in length, and the hypotenuse is √2 times the length of each leg.

Front

In a 30-60-90 triangle, what is the ratio of the lengths of the sides?

Back

The lengths are in the ratio 1:√3:2, where 1 is the length of the shorter leg, √3 is the length of the longer leg, and 2 is the hypotenuse.

Front

What is the length of the hypotenuse in a 45-45-90 triangle if each leg is 5 units long?

Back

The hypotenuse is 5√2 units long.

Front

What is the length of the longer leg in a 30-60-90 triangle if the shorter leg is 4 units long?

Back

The longer leg is 4√3 units long.

Front

What type of triangle is formed by two equal sides and a right angle?

Back

Isosceles right triangle.

Front

What is the measure of the angles in a 45-45-90 triangle?

Back

The angles measure 45 degrees, 45 degrees, and 90 degrees.

Front

What is the measure of the angles in a 30-60-90 triangle?

Back

The angles measure 30 degrees, 60 degrees, and 90 degrees.

Front

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

Back

The shorter leg is 5 units long.