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). Formula: a² + b² = c².

Front

How do you find the length of the missing side in a right triangle?

Back

To find the length of a missing side, use the Pythagorean Theorem. Rearrange the formula based on which side is missing: - If c is missing: c = √(a² + b²) - If a is missing: a = √(c² - b²) - If b is missing: b = √(c² - a²).

Front

What is a right triangle?

Back

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

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 a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

Back

Yes, it is a right triangle because 3² + 4² = 5² (9 + 16 = 25).

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

Use the Pythagorean Theorem: If a² + b² = c² holds true for the side lengths, then the triangle is a right triangle.

Front

What is the distance formula in the context of Pythagorean Theorem?

Back

The distance formula is derived from the Pythagorean Theorem and is used to find the distance between two points (x1, y1) and (x2, y2): Distance = √((x2 - x1)² + (y2 - y1)²).

Front

In a ladder problem, how do you find the height the ladder reaches?

Back

Use the Pythagorean Theorem: If the base of the ladder is d feet away from the wall and the ladder is l feet long, then height h can be found using h = √(l² - d²).

Front

What is the diagonal distance in a rectangle?

Back

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

Front

If John walks 6 blocks North and 8 blocks West, how do you find the straight-line distance back to school?

Back

Use the Pythagorean Theorem: Distance = √(6² + 8²) = √(36 + 64) = √100 = 10 blocks.