a 20-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 16ft from the base of the building. how high up the wall does the ladder reach?

Question

a 20-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 16ft from the base of the building. how high up the wall does the ladder reach?

Answer 1

Answer my question

Answer 2

To find out how high up the wall the ladder reaches, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.

Let's denote the height reached by the ladder as "h" (in feet).

According to the problem, the base of the ladder (the distance from the wall to the bottom of the ladder) is 16ft, and the ladder itself is 20ft.

Using the Pythagorean theorem, we can set up the following equation:

16^2 + h^2 = 20^2

Simplifying:

256 + h^2 = 400

Subtracting 256 from both sides:

h^2 = 400 - 256

h^2 = 144

To solve for "h", we take the square root of both sides:

h = √(144)

h = 12

Therefore, the ladder reaches a height of 12 feet up the wall.

Answer 3

To find out how high up the wall the ladder reaches, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this scenario, the ladder forms the hypotenuse, while the distance from the base of the building to the ladder and the height up the wall to which the ladder reaches are the other two sides of the triangle.

Let's assign variables:
- The distance from the base of the building to the ladder = x (unknown)
- The height up the wall the ladder reaches = y (unknown)
- The length of the ladder = 20 feet

According to the given information, x = 16 feet and the length of the ladder (hypotenuse), c = 20 feet.

Using the Pythagorean theorem, we can write the equation:

c^2 = a^2 + b^2

Substituting the values, we have:

20^2 = 16^2 + y^2

Simplifying the equation:

400 = 256 + y^2

Rearranging and isolating y^2:

y^2 = 400 - 256
y^2 = 144

Taking the square root of both sides:

y = √144
y = 12

Therefore, the ladder reaches a height of 12 feet up the wall.

Answer 4

a 20-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 16ft from the base of the building. how high up the wall does the ladder reach?

Answer my question

To find out how high up the wall the ladder reaches, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.

To find out how high up the wall the ladder reaches, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Use the Pythagorean Theorem as I showed you on the last problem. The hypotenuse is the length of the ladder.