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: c² = a² + b².

Front

How do you calculate the length of the diagonal of a rectangle using the Pythagorean Theorem?

Back

To calculate the length of the diagonal (d) of a rectangle with length (l) and width (w), use the formula: d = √(l² + w²).

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

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

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-degree angle, the longer leg is opposite the 60-degree angle, and the hypotenuse is the longest 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 can the Pythagorean Theorem be applied in real-life situations?

Back

The Pythagorean Theorem can be used in various real-life situations, such as determining distances, construction, navigation, and in fields like physics and engineering.

Front

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

Back

The distance (d) between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane can be calculated using the formula: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

How do you solve for a missing side in a right triangle using the Pythagorean Theorem?

Back

To solve for a missing side, rearrange the Pythagorean Theorem formula: If c is the hypotenuse and a or b is missing, use: a = √(c² - b²) or b = √(c² - a²).

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

What is an application of the Pythagorean Theorem in aviation?

Back

In aviation, the Pythagorean Theorem can be used to calculate the straight-line distance between two points when a plane travels north and then east.