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: c² = a² + b².

Front

How do you apply the Pythagorean Theorem to find the distance between two points?

Back

To find the distance between two points (x1, y1) and (x2, y2) on a coordinate plane, use the formula: Distance = √((x2 - x1)² + (y2 - y1)²). This is derived from the Pythagorean Theorem.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees. The side opposite the right angle is called the hypotenuse.

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

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

Back

Using the Pythagorean Theorem: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula is: Distance = √((x2 - x1)² + (y2 - y1)²). It calculates the distance between two points in a coordinate plane.

Front

How do you round numbers 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

In a word problem, how do you identify the right triangle?

Back

Look for a scenario involving two perpendicular lines or paths, which will form a right angle, indicating a right triangle.

Front

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

Back

The Pythagorean Theorem is used in various fields such as architecture, construction, navigation, and physics to calculate distances and ensure structures are built correctly.

Front

If a ladder is leaning against a wall, how can the Pythagorean Theorem be used?

Back

The ladder forms a right triangle with the wall and the ground. The length of the ladder is the hypotenuse, and the height it reaches on the wall and the distance from the wall to the base of the ladder are the other two sides.