Pythagorean Theorem Challenge

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 calculate the length of the hypotenuse in a right triangle?

Back

To calculate the length of the hypotenuse, use the formula c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

If one side of a right triangle is 3 units and the other side is 4 units, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 5 units, calculated using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

In a right triangle, if the lengths of the two legs are 6 units and 8 units, what is the length of the diagonal (hypotenuse)?

Back

The length of the diagonal (hypotenuse) is 10 units, calculated as c = √(6² + 8²) = √(36 + 64) = √100 = 10.

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 each leg.

Front

How do you find the distance from the top of a ladder to the base of a wall when the ladder is leaning against the wall?

Back

Use the Pythagorean Theorem: if the height of the ladder on the wall is h and the distance from the wall is d, then the length of the ladder (hypotenuse) can be found using c = √(h² + d²).

Front

If a ladder is 10 feet long and the base is 4 feet away from the wall, how high does it reach on the wall?

Back

The height reached on the wall can be calculated using the Pythagorean Theorem: h = √(10² - 4²) = √(100 - 16) = √84 ≈ 9.17 feet.

Front

What is the formula for the diagonal of a rectangle?

Back

The formula for the diagonal (d) of a rectangle is d = √(length² + width²).

Front

In a right triangle, if one leg is 9 feet and the hypotenuse is 15 feet, how do you find the length of the other leg?

Back

Use the Pythagorean Theorem: b = √(c² - a²), where c is the hypotenuse and a is the known leg. Here, b = √(15² - 9²) = √(225 - 81) = √144 = 12 feet.

Front

What is the significance of the Pythagorean Theorem in real-life applications?

Back

The Pythagorean Theorem is used in various real-life applications such as construction, navigation, and physics to determine distances and relationships between different points.