Pythagorean Theorem Word Problems Practice

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 feet and the other leg is 4 feet, what is the length of the hypotenuse?

Back

The hypotenuse is 5 feet, calculated using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5.

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 is given by: d = √((x2 - x1)² + (y2 - y1)²).

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.

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 1 is the length of the side 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.

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 and the distance from the wall is one leg, solve for the height (the other leg).

Front

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

Back

The area of a right triangle is given by: Area = (1/2) * base * height.