Pythagorean 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

What is a right triangle?

Back

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

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

5 feet (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

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

Front

How do you solve a Pythagorean word problem?

Back

1. Identify the right triangle in the problem. 2. Assign values to the sides. 3. 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. 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 length of the hypotenuse is √2 times the length of each leg.

Front

If a ladder is leaning against a wall and reaches a height of 12 feet while the base is 5 feet from the wall, how long is the ladder?

Back

13 feet (using the Pythagorean Theorem: 12² + 5² = 144 + 25 = 169; √169 = 13).

Front

What is the significance of the Pythagorean Theorem in real-life applications?

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.