Pythagorean Theorem & Distance Formula

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: a² + b² = c².

Front

What is a Pythagorean Triple?

Back

A Pythagorean Triple consists of three positive integers (a, b, c) that satisfy the Pythagorean Theorem, meaning a² + b² = c². An example is (3, 4, 5).

Front

Calculate the hypotenuse of a right triangle with legs of length 6 and 8.

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100. Therefore, c = √100 = 10.

Front

What is the Distance Formula?

Back

The Distance Formula is used to determine the distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane. It is given by: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

Find the distance between the points (3, 4) and (7, 1).

Back

Using the Distance Formula: d = √((7 - 3)² + (1 - 4)²) = √(4 + 9) = √13 ≈ 3.6.

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 side opposite the 30° angle is the shortest.

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 hypotenuse is √2 times the length of each leg.

Front

If one leg of a right triangle is 12 and the hypotenuse is 13, what is the length of the other leg?

Back

Using the Pythagorean Theorem: a² + 12² = 13². Therefore, a² + 144 = 169, so a² = 25, and a = 5.

Front

What is the significance of the Pythagorean Theorem in real life?

Back

The Pythagorean Theorem is used in various fields such as architecture, construction, navigation, and computer graphics to calculate distances and design structures.

Front

How do you determine if a set of three numbers is a Pythagorean Triple?

Back

To determine if a set of three numbers (a, b, c) is a Pythagorean Triple, check if a² + b² = c² holds true.