A building is 2ft from a 9ft fence that surrounds the property. A worker wants to wash a window in the building 13ft from the ground. he plans to place a ladder over the fence so it rests against the building. he decides he should place the ladder 8ft from the fence for stability. to the neares tenth of a foot, how long a ladder will he need?
Pythagorean Theorem:
13^2 + 10^2 = L^2
169 + 100 = L^2
269 = L^2
16.4 = L
Since the fence is mentioned, you really should check to see that the ladder will clear the fence. Using the given distances, and similar triangles, if the ladder lies on top of the fence, it will reach up to a height h, found by
9/8 = h/10
h = 12.5
In this case, the ladder clears the fence, since it is reaching up 13 ft.
Of course, in the real world, if I wanted to wash a window 13 ft up, I'd place the ladder a few feet below the window, so I don't have to bend down to wash the bottom, or lie along the ladder.
To determine the length of the ladder needed, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ladder is the hypotenuse, and the distance from the fence to the building is one side, while the vertical height of the window is the other side.
Let's call the distance from the fence to the building "x" and the vertical height of the window "y".
According to the problem, the ladder is placed 8ft from the fence, so x = 8ft.
Now, let's calculate the length of the ladder:
Using the Pythagorean theorem: x^2 + y^2 = ladder^2
Substituting the known values:
8^2 + 13^2 = ladder^2
Calculating:
64 + 169 = ladder^2
233 = ladder^2
To solve for the ladder, we take the square root of both sides:
√233 ≈ 15.26
Therefore, to the nearest tenth of a foot, the worker will need a ladder that is approximately 15.3 feet long.
To find the length of the ladder needed, we can use the Pythagorean theorem. According to the theorem, the square of the length of the ladder is equal to the sum of the squares of the distances from the base of the ladder to the fence and from the base of the ladder to the window.
Let's break down the given information:
1. The distance from the building to the fence is 2 ft.
2. The distance from the window to the ground is 13 ft.
3. The distance from the base of the ladder to the fence is 8 ft.
Using the Pythagorean theorem, we can calculate the length of the ladder:
Length of ladder^2 = (Distance to the fence)^2 + (Distance to the ground)^2
Length of ladder^2 = (2 ft)^2 + (13 ft)^2
= 4 ft^2 + 169 ft^2
= 173 ft^2
To find the length of the ladder, we take the square root of both sides of the equation:
Length of ladder = sqrt(173 ft^2)
≈ 13.1 ft
Therefore, the worker will need a ladder approximately 13.1 feet long to reach the window.