Special Right Triangles

Front

What are special right triangles?

Back

Special right triangles are triangles 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 is the relationship between the sides 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 equal to the length of a leg multiplied by √2.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the length of the side opposite the 30-degree angle is half the length of the hypotenuse, and the length of the side opposite the 60-degree angle is equal to the length of the side opposite the 30-degree angle multiplied by √3.

Front

If the hypotenuse of a 45-45-90 triangle is 10, what are the lengths of the legs?

Back

The lengths of the legs are each 10/√2 or 5√2.

Front

If the short side of a 30-60-90 triangle is 4, what are the lengths of the other sides?

Back

The length of the hypotenuse is 8, and the length of the longer side is 4√3.

Front

How do you find the length of the long side in a 45-45-90 triangle if the hypotenuse is known?

Back

Multiply the length of the hypotenuse by √2 and divide by 2.

Front

How do you find the length of the long side in a 30-60-90 triangle if the short side is known?

Back

Multiply the length of the short side by √3 to find the length of the longer side.

Front

What is the formula for the area of a right triangle?

Back

The area of a right triangle is given by the formula: Area = (1/2) * base * height.

Front

What is the Pythagorean theorem?

Back

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

Front

What is the value of √2 approximately?

Back

The value of √2 is approximately 1.414.