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

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

Front

If one leg of a right triangle measures 6 cm and the other leg measures 8 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 6² + 8² = c², which gives c = 10 cm.

Front

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

Back

Use the Pythagorean Theorem: 5² + b² = 13². Solve for b to find the length of the other leg.

Front

What is the formula to find the distance between two points in a coordinate plane using the Pythagorean Theorem?

Back

The distance d between two points (x1, y1) and (x2, y2) can be found using the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

How can the Pythagorean Theorem be applied to real-world problems?

Back

The Pythagorean Theorem can be used to determine distances, heights, and lengths in various real-world scenarios, such as construction, navigation, and sports.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse.

Front

If a ladder is leaning against a wall, how can you determine how high it reaches?

Back

You can use the Pythagorean Theorem: if the ladder is the hypotenuse and the distance from the wall is one leg, the height reached on the wall is the other leg.

Front

What is a common mistake when identifying the sides of a right triangle?

Back

A common mistake is to incorrectly identify the hypotenuse as one of the legs; the hypotenuse is always opposite the right angle and is the longest side.

Front

What is the significance of the right angle in a right triangle?

Back

The right angle (90 degrees) is crucial because it allows the use of the Pythagorean Theorem to relate the lengths of the sides.