pythagorean Theorem word problems

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.

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.

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5 feet.

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

Using the Pythagorean Theorem: c = 10, a = 6. So, b = √(10² - 6²) = √(100 - 36) = √64 = 8 feet.

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: d = √((x2 - x1)² + (y2 - y1)²).

Using the Pythagorean Theorem: c = √(5² + 12²) = √(25 + 144) = √169 = 13 feet.

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The shortest side is opposite the 30-degree angle.

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

Using the Pythagorean Theorem: b = √(15² - 9²) = √(225 - 81) = √144 = 12 feet.