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A building is 2 ft from an 8​-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 8 ft from the fence for stability. To the nearest tenth of a​ foot, how long a ladder will he​ need?

Respuesta :

The will need 16 feet now

Answer:

length of the ladder should be 16 feet.

Step-by-step explanation:

In the figure attached,

B is the window at 12 feet from the ground.

Building AB is 2 feet away from the fence DE.

Ladder AC is placed 8 feet away from the fence at a point C.

We apply Pythagoras theorem to calculate the length of the ladder.

AC² = AB² + BC²

AC = [tex]\sqrt{(12)^{2}+(2+8)^{2}}[/tex]

     = [tex]\sqrt{144+100}[/tex]

     = [tex]\sqrt{244}[/tex]

     = 15.62

     ≈ 16 feet

Therefore, length of the ladder should be 16 feet.

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