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

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

Back

The hypotenuse is x√2.

Front

How do you find the length of the longer leg in a 30-60-90 triangle if the shorter leg is x?

Back

The longer leg is x√3.

Front

How do you find the length of the hypotenuse in a 30-60-90 triangle if the shorter leg is x?

Back

The hypotenuse is 2x.

Front

If the hypotenuse of a 45-45-90 triangle is 10, what is the length of each leg?

Back

Each leg is 10/√2 or 5√2.

Front

If the longer leg of a 30-60-90 triangle is 12, what is the length of the shorter leg?

Back

The shorter leg is 12/√3 or 4√3.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (a² + b² = c²).

Front

How can you use the Pythagorean theorem with special right triangles?

Back

You can use the Pythagorean theorem to verify the side lengths of special right triangles based on their known ratios.