Pythagorean Theorem Word Problems Practice 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: a² + b² = c².

Front

What is a right triangle?

Back

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

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 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, the longer leg is opposite the 60-degree angle, and the hypotenuse is the longest side.

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 can be found using the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

How can the Pythagorean Theorem be applied in real-life situations?

Back

The Pythagorean Theorem can be used in various real-life situations, such as determining the length of a ladder needed to reach a certain height or finding the distance between two points.

Front

What is the formula for calculating the area of a right triangle?

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height.

Front

If a ladder is 15 feet long and reaches a height of 12 feet, how far is the base of the ladder from the wall?

Back

Using the Pythagorean Theorem: base = √(15² - 12²) = √(225 - 144) = √81 = 9 feet.

Front

What is the significance of the Pythagorean Theorem in geometry?

Back

The Pythagorean Theorem is fundamental in geometry as it establishes a relationship between the sides of right triangles, which is essential for solving various geometric problems.