Exploring the Pythagorean Theorem and Right Triangles

The video tutorial introduces the Pythagorean theorem, explaining its application to right triangles. It defines a right triangle and the hypotenuse, and demonstrates how to use the theorem to calculate unknown side lengths through three examples. The tutorial emphasizes understanding the theorem's formula and applying it to solve for different sides of a triangle, including simplifying radicals.

What is the fundamental relationship defined by the Pythagorean theorem for right triangles?

• a^2 + b^2 = c^2

• a^2 - b^2 = c^2

• a^2 + c^2 = b^2

• b^2 - a^2 = c^2

What is the hypotenuse in a right triangle?

• The shortest side of the triangle

• Any side of the triangle

• The side opposite the right angle

• The side adjacent to the right angle

If a right triangle has sides of 9 and 7, what is the length of the hypotenuse?

• 4

• 16

• Square root of 100

• Square root of 130

In a right triangle where one side is 21 and the hypotenuse is 35, what is the length of the unknown side?

• 49

• 7

• 14

• 28

How do you determine which side is the hypotenuse in a right triangle?

• It is the side with the largest square value

• It is always the shortest side

• It is the side adjacent to the right angle

• It is the side opposite the right angle

What is the correct calculation for the side of a right triangle if the hypotenuse is 35 and one side is 21?

• Square root of 625

• Square root of 256

• Square root of 144

• Square root of 784

What is the result of 24 squared minus 12 squared?

• 144

• 256

• 432

• 368

What is the simplified form of the square root of 784?

• 26

• 30

• 28

• 32

What is the length of side b if it is calculated as the square root of 432?

• 18

• 20

• 15

• 12 times the square root of 3

How can the square root of 216 be simplified?

• 6 times the square root of 6

• 12 times the square root of 3

• 9 times the square root of 4

• 4 times the square root of 14