Word Problems: Pythagorean Theorem

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

Back

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

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 side opposite the 30° angle is the shortest, the side opposite the 60° angle is √3 times the shortest side, and the hypotenuse is twice the shortest side.

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 one leg.

Front

How do you apply the Pythagorean Theorem to real-world problems?

Back

Identify the right triangle in the problem, label the sides, and use the Pythagorean Theorem to find the unknown side length.

Front

What is the formula to calculate the distance between two points in a coordinate plane?

Back

The distance formula is: d = √((x₂ - x₁)² + (y₂ - y₁)²), where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Front

If a ladder is leaning against a wall, how can you find the height it reaches on the wall?

Back

Use the Pythagorean Theorem, where the length of the ladder is the hypotenuse, the distance from the wall is one leg, and the height on the wall is the other leg.

Front

What is the significance of rounding in measurements?

Back

Rounding is important in measurements to ensure that the values are practical and manageable, especially when dealing with real-world applications.

Front

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

If the lengths of the sides satisfy the equation a² + b² = c², where c is the longest side, then the triangle is a right triangle.