Pythagorean Theorem LAB - Practice

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 determine if a set of three numbers can form a right triangle?

Back

To determine if three numbers can form a right triangle, check if the square of the largest number equals the sum of the squares of the other two numbers. If a² + b² = c² holds true, then they can form a right triangle.

Front

What is the length of the diagonal of a rectangle with length 12 inches and width 5 inches?

Back

Using the Pythagorean Theorem: c = √(12² + 5²) = √(144 + 25) = √169 = 13 inches.

Front

If a ladder is 50 ft long and its base is 30 ft away from a wall, how high does it reach on the wall?

Back

Using the Pythagorean Theorem: height = √(50² - 30²) = √(2500 - 900) = √1600 = 40 ft.

Front

What is the distance from point A to point B if a spectator is 1,500 meters away from point C and the contestants row 2,112 meters?

Back

Using the Pythagorean Theorem: distance = √(2112² + 1500²) = √(4460544 + 2250000) = √(6710544) ≈ 2,590 meters.

Front

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

Back

In a right triangle, the relationship between the lengths of the sides is defined by the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

How much shorter is the direct walk if William walks 6 blocks north and 8 blocks west?

Back

Using the Pythagorean Theorem: direct distance = √(6² + 8²) = √(36 + 64) = √100 = 10 blocks. His walk is 10 - (6 + 8) = 4 blocks shorter.

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

What is the formula to calculate the area of a right triangle?

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height.