Pythagorean Theorem Application

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 in a right triangle?

Back

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

Front

If one side of a right triangle is 3 ft and the other side is 4 ft, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5 ft.

Front

What is the relationship between the sides 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. The shortest side is opposite the 30° angle, the longer leg is opposite the 60° angle, and the hypotenuse is twice the shortest side.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane is: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

How can the Pythagorean Theorem be applied in real life?

Back

The Pythagorean Theorem can be used in various real-life situations, such as determining the height of a ladder against a wall, finding the shortest distance between two points, or in construction to ensure structures are level.

Front

What is the significance of the Pythagorean Theorem in geometry?

Back

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

Front

If a ladder is 10 ft long and it reaches a height of 6 ft on a wall, how far is the base of the ladder from the wall?

Back

Using the Pythagorean Theorem: c = 10 ft, b = 6 ft. Therefore, a = √(10² - 6²) = √(100 - 36) = √64 = 8 ft.

Front

What is the maximum diameter of an object that can fit through a rectangular door that is 42 inches wide?

Back

The maximum diameter of an object that can fit through the door is 42 inches, as it cannot exceed the width of the door.

Front

In a right triangle, if one leg is 5 cm and the hypotenuse is 13 cm, what is the length of the other leg?

Back

Using the Pythagorean Theorem: c = 13 cm, a = 5 cm. Therefore, b = √(13² - 5²) = √(169 - 25) = √144 = 12 cm.