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 a missing side in a right triangle using the Pythagorean Theorem?

Back

To find the length of a missing side, rearrange the Pythagorean Theorem formula. If you know the lengths of the other two sides, you can solve for the missing side by using: a = √(c² - b²) or b = √(c² - a²).

Front

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

Back

In a right triangle, the side opposite the right angle is the hypotenuse, and it is always the longest side. The other two sides are referred to as the legs.

Front

What is the formula to calculate the distance traveled when moving in perpendicular directions?

Back

When moving in perpendicular directions, the total distance can be calculated using the Pythagorean Theorem. If you travel a distance 'a' in one direction and 'b' in another, the total distance 'd' is given by: d = √(a² + b²).

Front

If one leg of a right triangle is 30 units and the other leg is 40 units, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(30² + 40²) = √(900 + 1600) = √2500 = 50 units.

Front

What is the significance of the Pythagorean Theorem in real-world applications?

Back

The Pythagorean Theorem is used in various real-world applications, including construction, navigation, and physics, to determine distances and relationships between points.

Front

How can the Pythagorean Theorem be applied to find the height of a triangle?

Back

To find the height of a triangle, you can use the Pythagorean Theorem by creating a right triangle where the height is one leg, the base is the other leg, and the hypotenuse is the slant height.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula, which calculates the distance between two points (x1, y1) and (x2, y2) in a coordinate plane, is derived from the Pythagorean Theorem: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the relationship between the Pythagorean Theorem and trigonometry?

Back

The Pythagorean Theorem is foundational for trigonometry, as it relates the lengths of the sides of right triangles to the angles, allowing for the definition of sine, cosine, and tangent.

Front

What is a common mistake when applying the Pythagorean Theorem?

Back

A common mistake is to confuse the hypotenuse with one of the legs or to incorrectly apply the theorem to non-right triangles.