#3✏️WK 17Wed.12/13/23 HW#3:Flashcardizz Pythagorean Thm word problems

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: a² + b² = c².

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

If one side of a right triangle is 6 feet and the other side is 8 feet, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10 feet.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

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 the longest side. The other two sides are called the legs.

Front

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

Back

You can determine if a triangle is a right triangle by checking if the lengths of the sides satisfy the Pythagorean Theorem: a² + b² = c².

Front

What is the distance formula in a coordinate plane?

Back

The distance formula is derived from the Pythagorean Theorem and is used to find the distance between two points (x₁, y₁) and (x₂, y₂): d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

If a ladder is placed 10 feet away from a wall and reaches a height of 25 feet, how long is the ladder?

Back

Using the Pythagorean Theorem: c = √(10² + 25²) = √(100 + 625) = √725 ≈ 26.93 feet.

Front

What is the formula for the area of a right triangle?

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) × base × height.

Front

If Jane walks 6 blocks east and Miguel walks 8 blocks north, how far apart are they?

Back

Using the Pythagorean Theorem: d = √(6² + 8²) = √(36 + 64) = √100 = 10 blocks.