8.9b Applying Pythagorean Theorem

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). It can be expressed as: c² = a² + b².

Front

How do you find the length of the hypotenuse using the Pythagorean Theorem?

Back

To find the length of the hypotenuse, rearrange the Pythagorean Theorem formula to c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

If one leg of a right triangle is 7 feet and the other leg is 4 feet, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(7² + 4²) = √(49 + 16) = √65.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the lengths of the sides must satisfy the Pythagorean Theorem, meaning the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

How can the Pythagorean Theorem be applied in real-life situations?

Back

The Pythagorean Theorem can be used in various real-life situations such as determining the length of a ladder needed to reach a certain height, calculating distances in navigation, and in construction to ensure structures are level.

Front

What is the formula for calculating the area of a square?

Back

The area of a square is calculated using the formula: Area = side², where 'side' is the length of one side of the square.

Front

If the area of one square is 369 and the area of another is 81, how do you find the area of the missing square off of leg A?

Back

To find the area of the missing square, use the Pythagorean Theorem: Area of missing square = Area of square on hypotenuse - (Area of square on leg A + Area of square on leg B). In this case, it would be 369 - (369 - 81) = 288.

Front

What is the diagonal of a rectangle and how is it calculated?

Back

The diagonal of a rectangle can be calculated using the Pythagorean Theorem: d = √(length² + width²), where 'length' and 'width' are the dimensions of the rectangle.

Front

In a right triangle, if one leg is 15 inches and the other leg is 20 inches, what is the length of the diagonal?

Back

Using the Pythagorean Theorem: d = √(15² + 20²) = √(225 + 400) = √625 = 25 inches.

Front

What is the significance of the Pythagorean Theorem in geometry?

Back

The Pythagorean Theorem is fundamental in geometry as it establishes the relationship between the sides of right triangles, which is essential for various geometric proofs and applications.