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: 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 (c) is: c = √(a² + b²), where a and b are the lengths of the other two sides.

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

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, the side opposite the 60° angle is √3 times the shortest side, and the hypotenuse is twice the shortest side.

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

How do you find the length of one side of a right triangle if the hypotenuse and one side are known?

Back

You can rearrange the Pythagorean Theorem: If c is the hypotenuse and a is one side, then b = √(c² - a²).

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

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

Back

Using the Pythagorean Theorem: c = √(5² + 12²) = √(25 + 144) = √169 = 13.

Front

What is the area of a right triangle?

Back

The area (A) of a right triangle can be calculated using the formula: A = (1/2) * base * height.

Front

If the height of a slide is 6 feet and the base is 8 feet, what is the length of the slide?

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10 feet.