Mr. Clark leaned a ladder against a wall. When placed, the ladder reaches the top of the wall. If the ladder is 35 feet long, and Mr. Allen places the ladder 28 feet from the wall, how tall is the wall? Use the picture below to help you. Show ALL of your work

Answer 1

We can use the Pythagorean theorem to solve the problem. Let's label the ladder as c, the distance from the wall as a, and the height of the wall as b.

a² + b² = c²

We know that c (the ladder) is 35 feet long, and a (the distance from the wall) is 28 feet. We want to find b (the height of the wall).

28² + b² = 35²

784 + b² = 1225

b² = 441

b = √441

b = 21

Therefore, the wall is 21 feet tall.

Answer 2

To find the estimate of 68−−√
what two square roots should you use?

Answer 3

We can estimate the value of √68 by finding the two perfect squares that 68 is between, and taking the square roots of those perfect squares.

68 is between 64 (8²) and 81 (9²):

8² = 64
9² = 81

Since 68 is closer to 64 than 81, we can estimate that:

√68 ≈ √64 = 8

Note that this is only an estimate, and the actual value of √68 is a non-repeating decimal (approximately 8.2462).

Answer 4

To find the estimate of 68−−√
what two square roots should you use?
Responses

Answer 5

We can estimate the value of √68 by finding the two perfect squares that 68 is between, and taking the square roots of those perfect squares.

68 is between 64 (8²) and 81 (9²):

8² = 64
9² = 81

Since 68 is closer to 64 than 81, we can estimate that:

√68 ≈ √64 = 8

Note that this is only an estimate, and the actual value of √68 is a non-repeating decimal (approximately 8.2462).