Applying Pythagorean Theorem

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 a right triangle?

Back

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

Front

How do you find the height of a ladder leaning against a wall?

Back

Use the Pythagorean Theorem: if the ladder is the hypotenuse (c) and the distance from the wall is one side (a), then the height (b) can be found using b = √(c² - a²).

Front

If a ladder is 12 feet long and the base is 8 feet from the wall, how high does it reach?

Back

Using the Pythagorean Theorem: b = √(12² - 8²) = √(144 - 64) = √80 ≈ 8.9 feet.

Front

What is the formula to find the diagonal of a rectangle?

Back

The diagonal (d) can be found using the Pythagorean Theorem: d = √(length² + width²).

Front

If a soccer field is 90 meters wide and 120 meters long, what is the diagonal distance?

Back

Using the Pythagorean Theorem: d = √(120² + 90²) = √(14400 + 8100) = √22500 = 150 meters.

Front

What does 'hypotenuse' mean?

Back

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

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 shorter sides equals the square of the hypotenuse (a² + b² = c²).

Front

How do you determine the width of a TV given its diagonal and height?

Back

Use the Pythagorean Theorem: if the diagonal is c and the height is a, then the width (b) can be found using b = √(c² - a²).

Front

If a TV has a diagonal of 40 inches and a height of 30 inches, what is the width?

Back

Using the Pythagorean Theorem: b = √(40² - 30²) = √(1600 - 900) = √700 ≈ 26.5 inches.