Pythagorean Theorem Applications

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 a missing side in a right triangle?

Back

To find the length of a missing side in a right triangle, use the Pythagorean Theorem: c² = a² + b². Rearrange the formula to solve for the missing side.

Front

If one side of a right triangle is 6 cm and the other side is 8 cm, what is the length of the hypotenuse?

Back

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

Front

What is the diagonal length of a square with a side length of 10 units?

Back

The diagonal (d) of a square can be found using the formula: d = s√2, where s is the side length. For a side length of 10 units, d = 10√2 ≈ 14.14 units.

Front

How do you calculate the area of a square?

Back

The area (A) of a square is calculated by squaring the length of one of its sides: A = s².

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 opposite the 90° angle.

Front

If a right triangle has legs of lengths 5 cm and 12 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169. Therefore, c = √169 = 13 cm.

Front

What is the formula for the distance between two points in a coordinate plane?

Back

The distance (d) between two points (x₁, y₁) and (x₂, y₂) is given by the formula: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

How do you find the length of the diagonal of a rectangle?

Back

The length of the diagonal (d) of a rectangle can be found using the Pythagorean Theorem: d = √(length² + width²).

Front

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

Back

The Pythagorean Theorem is used in various real-life applications, such as construction, navigation, and computer graphics, to calculate distances and ensure structures are built correctly.