A building is 2ft from a 9ft fence that surrounds the property.A worker wants to wash a window in the building 13 ft 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 7ft from the fence for stability. To the nearest tenth of foot how long a ladder will he need
L = Sqrt(x^2+Y^2) = Sqrt(9^2+13^2) = 15.8 Ft.
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 longest side) is equal to the sum of the squares of the other two sides.
In this scenario, the ladder, the distance between the fence and the building, and the ground form a right triangle. Let's label the sides as follows:
1. The distance from the fence to the building: 2ft
2. The distance from the ground to the window: 13ft
3. The distance from the fence to the point where the ladder rests against the building (let's call this distance 'x')
According to the given information, the worker plans to place the ladder 7ft from the fence for stability. Therefore, the base of the right triangle (the distance from the point where the ladder rests against the building to the window) is the sum of the distances from the fence to the ladder's placement point and from the fence to the building:
Base = (distance from the fence to the ladder's placement point) + (distance from the fence to the building) = x + 2
With this information, we can now apply the Pythagorean theorem:
Hypotenuse^2 = Base^2 + Height^2
Ladder^2 = (x + 2)^2 + 13^2
Ladder^2 = x^2 + 4x + 4 + 169
Ladder^2 = x^2 + 4x + 173
To find the length of the ladder, we need to take the square root of both sides of the equation:
Ladder = sqrt(x^2 + 4x + 173)
Now that we have an equation that represents the length of the ladder, we can substitute the value of x with 7 (as given in the question) and calculate the result:
Ladder = sqrt(7^2 + 4(7) + 173)
Ladder = sqrt(49 + 28 + 173)
Ladder = sqrt(250)
Ladder ≈ 15.8 ft
Therefore, to the nearest tenth of a foot, the worker would need a ladder approximately 15.8 ft long.