Special Right Triangles

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures that allow for easy calculation of side lengths. The two main types are 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 lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of a leg.

Front

If the length of a leg in a 45-45-90 triangle is x, what is the length of the hypotenuse?

Back

The length of the hypotenuse is x√2.

Front

What are the side ratios of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, where 1 is the length of the side opposite the 30-degree angle, √3 is opposite the 60-degree angle, and 2 is the hypotenuse.

Front

If the length of the side opposite the 30-degree angle in a 30-60-90 triangle is x, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 2x.

Front

If the length of the hypotenuse in a 30-60-90 triangle is y, what is the length of the side opposite the 30-degree angle?

Back

The length of the side opposite the 30-degree angle is y/2.

Front

If the length of the side opposite the 60-degree angle in a 30-60-90 triangle is z, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 2z/√3.

Front

What is the formula to find the length of the hypotenuse in a 45-45-90 triangle if the leg length is known?

Back

Hypotenuse = leg length × √2.

Front

What is the formula to find the length of the longer leg in a 30-60-90 triangle if the shorter leg length is known?

Back

Longer leg = shorter leg × √3.

Front

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

Back

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