Question

a building is 3 ft from a 7 - 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 7 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 horizontal distance

The horizontal distance from the base of the ladder to the building is the sum of the distance from the fence to the building ($3$ ft) and the distance from the base of the ladder to the fence ($7$ ft), so it is $3 + 7=10$ ft.

Step2: Calculate vertical distance

The vertical distance from the top - of - the fence to the window is $12$ ft.

Step3: Apply Pythagorean theorem

The length of the ladder $L$ forms the hypotenuse of a right - triangle, where the horizontal side $a = 10$ ft and the vertical side $b = 12$ ft. According to the Pythagorean theorem $L=\sqrt{a^{2}+b^{2}}=\sqrt{10^{2}+12^{2}}=\sqrt{100 + 144}=\sqrt{244}\approx15.6$ ft.

Answer:

$15.6$