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: 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

In a right triangle, if one leg is 5 feet and the hypotenuse is 13 feet, what is the length of the other leg?

Back

Using the Pythagorean Theorem: b = √(c² - a²) = √(13² - 5²) = √(169 - 25) = √144 = 12 feet.

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 length of the hypotenuse is √2 times the length of one leg.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula between two points (x1, y1) and (x2, y2) is: d = √((x2 - x1)² + (y2 - y1)²).

Front

If a ladder is 10 feet away from a wall and reaches a height of 24 feet, what is the length of the ladder?

Back

Using the Pythagorean Theorem: c = √(10² + 24²) = √(100 + 576) = √676 = 26 feet.

Front

What is the diagonal distance across a square with sides of 10 feet?

Back

Using the Pythagorean Theorem: d = √(10² + 10²) = √(100 + 100) = √200 = 14.14 feet.

Front

How do 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 a² + b² = c² holds true for the lengths of the sides.