Pythagorean Word Probz

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 can you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if the lengths of the sides satisfy the Pythagorean Theorem: c² = a² + b², where c is the longest side (hypotenuse). If the equation holds true, the triangle is a right triangle.

Front

What is the formula to calculate the height reached by a ladder leaning against a wall?

Back

The height (h) reached by a ladder can be calculated using the Pythagorean Theorem: h = √(l² - d²), where l is the length of the ladder and d is the distance from the base of the ladder to the wall.

Front

If a ladder is 13 feet long and placed 5 feet away from a wall, how high does it reach?

Back

Using the Pythagorean Theorem: h = √(13² - 5²) = √(169 - 25) = √144 = 12 feet.

Front

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

Back

In a right triangle, the relationship between the lengths of the sides is defined by the Pythagorean Theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

How do you find the length of a side in a right triangle if you know the lengths of the other two sides?

Back

You can find the length of the unknown side using the Pythagorean Theorem. For example, if you know a and b, you can find c using c = √(a² + b²). If you know c and one side, you can find the other side using a = √(c² - b²) or b = √(c² - a²).

Front

What is the distance formula 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

In the context of the ladder problem, what does the base distance represent?

Back

The base distance represents the horizontal distance from the base of the ladder to the wall, which is used to calculate the height the ladder reaches using the Pythagorean Theorem.

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 can you apply the Pythagorean Theorem to real-world problems?

Back

The Pythagorean Theorem can be applied to real-world problems involving right triangles, such as calculating heights, distances, and lengths in construction, navigation, and various fields of engineering.