Pythagorean Theorem - Distance and 3D Figures

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 calculate the distance between two points in a 2D plane?

Back

To calculate the distance between two points (x1, y1) and (x2, y2) in a 2D plane, use the distance formula: Distance = √((x2 - x1)² + (y2 - y1)²).

Front

What is the distance formula in 3D space?

Back

In 3D space, the distance between two points (x1, y1, z1) and (x2, y2, z2) is calculated using the formula: Distance = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²).

Front

If a triangle has sides of lengths 3 in. and 4 in., what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25. Therefore, c = √25 = 5 in.

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

How do you find the length of a diagonal in a rectangular prism?

Back

To find the length of the diagonal (d) in a rectangular prism with length (l), width (w), and height (h), use the formula: d = √(l² + w² + h²).

Front

What is the formula for 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 a frisbee travels 244 feet, how can you express this distance in meters?

Back

To convert feet to meters, use the conversion factor: 1 foot = 0.3048 meters. Therefore, 244 feet × 0.3048 = 74.43 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, and is crucial for applying the Pythagorean Theorem.

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

To determine if a triangle with sides a, b, and c (where c is the longest side) is a right triangle, check if a² + b² = c².