A building is 1ft from an 11ft fence that surrounds the property. A worker wants to wash a awindow in the building 14ft from the ground. he plans to place the ladder over the fence so it rests against the building. He decides he should decides to place the ladder 10ft from the fence for stability. To the nearest tenth of a foot, how long a ladder will he need
I assume we're dealing with point-size worker and window, and that the ladder will just touch the window. try using that setup in real life!
Draw a diagram. You have a right triangle with sides 11 and 14
ladder must be sqrt(121+196) = 17.8 ft
The height of the fence is not relevant, as long as it is less than 10/11*14 = 12.72 ft. Any higher than that, and the ladder will rest on the fence, not against the building.
18.4
To figure out the length of the ladder needed, we can use the Pythagorean theorem, which states that in a right 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 forms a right triangle with the ground, the fence, and the building. The ladder will act as the hypotenuse of this triangle, with the distance from the building to the fence being one side, and the height at which the worker wants to wash the window being the other side.
Let's calculate the length of the ladder using the Pythagorean theorem:
Distance from the building to the fence = 1 ft
Height at which the worker wants to wash the window = 14 ft
Using the Pythagorean theorem: (Length of ladder)^2 = (Distance from the building to the fence)^2 + (Height at which the worker wants to wash the window)^2
Length of ladder = sqrt((Distance from the building to the fence)^2 + (Height at which the worker wants to wash the window)^2)
Length of ladder = sqrt((1 ft)^2 + (14 ft)^2)
Length of ladder = sqrt(1 ft^2 + 196 ft^2)
Length of ladder = sqrt(197 ft^2)
Length of ladder ≈ 14 ft (rounded to the nearest tenth of a foot)
Therefore, the worker will need a ladder that is approximately 14 feet long.
To determine the length of the ladder needed, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length 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 distance between the building and the fence forms the base of the right triangle, and the height of the ladder needed to reach the window forms the other side of the triangle. We need to find the length of the hypotenuse (the ladder).
Let's break down the given information:
- The building is 1ft from the fence.
- The ladder will be placed 10ft from the fence.
- The height of the window from the ground is 14ft.
Now, let's calculate the distance between the building and the ladder.
The distance between the building and the ladder is the sum of the distance between the building and the fence (1ft) and the distance between the fence and the ladder (10ft). So, the base of the triangle is 1ft + 10ft = 11ft.
Now, we can calculate the length of the ladder using the Pythagorean theorem:
Length of ladder = √(base^2 + height^2)
= √(11^2 + 14^2)
≈ √(121 + 196)
≈ √(317)
≈ 17.8ft (rounded to the nearest tenth)
Therefore, the worker will need a ladder that is approximately 17.8ft long to reach the window.