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 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 a right triangle?

Back

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

Front

In a right triangle, if one leg is 5 units and the hypotenuse is 13 units, how do you find the other leg?

Back

Use the Pythagorean Theorem: b = √(c² - a²) = √(13² - 5²) = √(169 - 25) = √144 = 12 units.

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

If a ladder is 10 feet long and the base is 6 feet from the wall, how high does it reach?

Back

Using the Pythagorean Theorem: h = √(10² - 6²) = √(100 - 36) = √64 = 8 feet.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the legs are equal in length, and the hypotenuse is √2 times the length of each leg.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the length of the side opposite the 30-degree angle is half the length of the hypotenuse, and the length of the side opposite the 60-degree angle is √3 times the length of the shorter leg.