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 a and b are the lengths of the other two sides.

Front

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

Back

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

Front

What is a right triangle?

Back

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

Front

In a Pythagorean Theorem word problem, what do you typically need to find?

Back

You typically need to find the length of one side of a right triangle or the hypotenuse, given the lengths of the other two sides.

Front

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

Back

It can be used in various situations such as determining the distance between two points, calculating heights, and in construction to ensure structures are level.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula is d = √((x₂ - x₁)² + (y₂ - y₁)²), which calculates the distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane.

Front

If a ladder is placed 10 feet away from a wall and reaches a height of 25 feet, how long is the ladder?

Back

Using the Pythagorean Theorem: c = √(10² + 25²) = √(100 + 625) = √725 ≈ 26.9 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, where the shortest side is opposite the 30-degree angle.

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 hypotenuse is √2 times the length of each leg.