Ladder Problem and Pythagorean Theorem

The video tutorial explains the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It provides examples of calculating the hypotenuse and a missing leg in a triangle. The tutorial also demonstrates a real-world application of the theorem, where a firefighter uses a ladder to rescue a cat from a tree, illustrating how to calculate the height of the cat using the theorem.

What is the primary use of the Pythagorean theorem?

• To determine the volume of a cube

• To measure the circumference of a square

• To find the length of sides in a right triangle

• To calculate the area of a circle

Which of the following represents the Pythagorean theorem?

• a² + b² = c

• a² + b² = c²

• a + b = c²

• a² = b² + c²

In a right triangle, if one leg is 3 and the other is 4, what is the length of the hypotenuse?

• 8

• 5

• 6

• 7

If a right triangle has legs of 3 and 4, what is the value of 3² + 4²?

• 12

• 16

• 25

• 30

What is the first step in solving for the hypotenuse in a right triangle?

• Subtract the squares of the legs

• Add the squares of the legs

• Multiply the legs

• Divide the legs

In a right triangle with one leg of 3.2 and a hypotenuse of 4.2, what is the length of the other leg rounded to the nearest tenth?

• 3.5

• 2.7

• 3.0

• 4.0

What is the value of 3.2²?

• 9.24

• 10.24

• 11.24

• 12.24

What is the value of 4.2²?

• 16.64

• 18.64

• 17.64

• 19.64

In the ladder problem, what is the length of the ladder?

• 8 meters

• 9 meters

• 10 meters

• 11 meters

How far is the base of the ladder from the tree in the ladder problem?

• 4.1 meters

• 3.1 meters

• 2.1 meters

• 5.1 meters