Question

a building is 1 ft from a 9 - ft fence that surrounds the property. a worker wants to wash a window in the building 12 ft from the ground. he plans to place a ladder over the fence so it rests against the building. (see the figure.) he decides he should place the ladder 9 ft from the fence for stability. to the nearest tenth of a foot, how long a ladder will he need? he will need a ft ladder. (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Calculate the horizontal distance

The horizontal distance from the bottom of the ladder to the building is \(9 + 1=10\) ft.

Step2: Calculate the vertical distance

The vertical distance from the ground to the window is \(12\) ft.

Step3: Use the Pythagorean theorem

The length \(L\) of the ladder is the hypotenuse of a right - triangle with legs \(a = 10\) ft and \(b = 12\) ft. According to the Pythagorean theorem \(L=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 10\) and \(b = 12\) into the formula: \(L=\sqrt{10^{2}+12^{2}}=\sqrt{100 + 144}=\sqrt{244}\).

Step4: Simplify the square - root

\(\sqrt{244}\approx15.6\) (using a calculator, \(\sqrt{244}=\sqrt{4\times61}=2\sqrt{61}\approx2\times7.81 = 15.62\approx15.6\))

Answer:

\(15.6\)