Pythagorean Theorem Word Problems Flashcard 1

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

What is a right triangle?

Back

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

Front

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

Back

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

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 twice the shortest side.

Front

How do you round a number to the nearest tenth?

Back

To round a number to the nearest tenth, look at the hundredths place. If it is 5 or greater, round up the tenths place by one. If it is less than 5, keep the tenths place the same.

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: if the ladder is the hypotenuse (c) and the distance from the wall is one leg (a), then the height (b) can be found using b = √(c² - a²).

Front

What is the significance of the diagonal in a rectangle?

Back

The diagonal of a rectangle can be calculated using the Pythagorean Theorem, as it forms two right triangles within the rectangle.

Front

How do you solve a word problem involving the Pythagorean Theorem?

Back

Identify the right triangle, assign values to the legs and hypotenuse, and apply the Pythagorean Theorem to find the unknown side.