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 that make calculations easier. 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 legs are of equal length, and the hypotenuse is √2 times the length of each leg.

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 the length of the side opposite the 60-degree angle, and 2 is the hypotenuse.

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 to find the hypotenuse.

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 (opposite the 30-degree angle) by √3 to find the longer leg (opposite the 60-degree angle).

Front

What is the relationship between the legs in an isosceles right triangle?

Back

The legs of an isosceles right triangle are equal in length.

Front

If one leg of a 45-45-90 triangle is 4, what is the length of the hypotenuse?

Back

The hypotenuse is 4√2.

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

What type of triangle is formed by angles of 30°, 60°, and 90°?

Back

A 30-60-90 triangle.

Front

What type of triangle is formed by angles of 45°, 45°, and 90°?

Back

A 45-45-90 triangle.