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 the formula to find the length of the hypotenuse in a right triangle?

Back

The formula to find the length of the hypotenuse is c = √(a² + b²).

Front

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

Back

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

Front

In a right triangle, if the lengths of the two legs are 6 and 8, what is the length of the hypotenuse?

Back

c = √(6² + 8²) = √(36 + 64) = √100 = 10 units.

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if a² + b² = c² holds true for the lengths of the sides.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

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

Front

If a rectangular field is 50 yards wide and 100 yards long, how do you find the diagonal distance?

Back

Use the Pythagorean Theorem: d = √(50² + 100²) = √(2500 + 10000) = √12500 ≈ 111.8 yards.

Front

What is the height of a hot air balloon if it is 20 meters away from a point on the ground and the distance between them is 20 meters?

Back

Using the Pythagorean Theorem: h = √(20² - 16²) = √(400 - 256) = √144 = 12 meters.

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.