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
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.
To find the estimate of 68−−√
what two square roots should you use?
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).
To find the estimate of 68−−√
what two square roots should you use?
Responses
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).
To solve this problem, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, and the wall acts as one of the other two sides. So, we have:
Ladder^2 = Wall^2 + Distance^2,
35^2 = Wall^2 + 28^2.
Solving for Wall:
1225 = Wall^2 + 784,
Wall^2 = 1225 - 784,
Wall^2 = 441.
Taking the square root of both sides to find the value of Wall:
Wall = √441,
Wall = 21.
Therefore, the height of the wall is 21 feet.
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle (such as the one formed by the ladder, the wall, and the ground), the square of the length of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides (the distance of the ladder from the wall and the height of the wall).
Given that the ladder is 35 feet long and placed 28 feet from the wall, we need to find the height of the wall.
Using the Pythagorean theorem, we have:
35^2 = 28^2 + height^2
Simplifying the equation:
1225 = 784 + height^2
Rearranging the equation:
height^2 = 1225 - 784
height^2 = 441
Taking the square root of both sides to solve for height:
height = √441
height = 21 feet
Therefore, the height of the wall is 21 feet.