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 find the length of the hypotenuse in a right triangle?

Back

To find the length of the hypotenuse, use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the other two sides.

Front

What is the formula to find the length of a side in a right triangle if the hypotenuse and one side are known?

Back

If the hypotenuse (c) and one side (a) are known, the length of the other side (b) can be found using the formula: 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 Cartesian plane is: d = √((x2 - x1)² + (y2 - y1)²).

Front

How can the Pythagorean Theorem be applied to real-world problems?

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

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, 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 calculate the diagonal of a rectangle using the Pythagorean Theorem?

Back

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

Front

What is the significance of the Pythagorean Theorem in coordinate geometry?

Back

In coordinate geometry, the Pythagorean Theorem is used to calculate distances between points, determine the lengths of sides of triangles formed by points, and analyze geometric properties.

Front

What is an example of a problem that can be solved using the Pythagorean Theorem?

Back

An example problem: A ladder is leaning against a wall. If the base of the ladder is 4 feet from the wall and the ladder is 5 feet long, how high does it reach on the wall? (Use the Pythagorean Theorem to find the height.)