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 3 feet and the other side is 4 feet, what is the length of the hypotenuse?

Back

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

Front

What is a right triangle?

Back

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

Front

In a ladder problem, if the ladder is 10 feet long and the base is 6 feet from the wall, how high does the ladder reach?

Back

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

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

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

Front

If a slide is 5 feet high and the base is 12 feet away from the wall, how long is the slide?

Back

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

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

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.

Front

If John walks 8 blocks north and 6 blocks east, how far is he from the starting point?

Back

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

Front

What is the height of a right triangle if the base is 9 feet and the hypotenuse is 15 feet?

Back

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