pythagorean theorem 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: c² = a² + b².

Front

How do you identify a right triangle?

Back

A right triangle is identified by having one angle that measures exactly 90 degrees.

Front

What is the formula to calculate the length of the hypotenuse in a right triangle?

Back

The length of the hypotenuse can be calculated using the formula: c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the other two sides.

Front

In a word problem, how can you determine if the Pythagorean Theorem can be applied?

Back

You can apply the Pythagorean Theorem if the problem involves a right triangle and provides the lengths of two sides or requires finding the length of the hypotenuse.

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides are in the ratio 3:4:5, which satisfies the Pythagorean Theorem (3² + 4² = 5²). This is a common example of a right triangle.

Front

How do you find the distance between two points in a coordinate plane?

Back

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

Front

What is the significance of the diagonal in a rectangle?

Back

The diagonal of a rectangle can be calculated using the Pythagorean Theorem, as it forms a right triangle with the length and width of the rectangle.

Front

How can you apply the Pythagorean Theorem to real-life situations?

Back

The Pythagorean Theorem can be applied in various real-life situations, such as determining distances in navigation, construction, and design, where right triangles are involved.

Front

What is the length of the diagonal of a TV screen if the width is known?

Back

The length of the diagonal (d) can be calculated using the formula: d = √(width² + height²), where width and height are the dimensions of the screen.

Front

How do you solve for one side of a right triangle if the hypotenuse and one side are known?

Back

You can solve for the unknown side using the rearranged Pythagorean Theorem: a = √(c² - b²) or b = √(c² - a²), depending on which side is unknown.