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A building is 3 ft from an 8​-ft 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.​ (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?

Answer :

Answer:

Length of the ladder used by worker = 17 feet

Step-by-step explanation:

Given:

Height of the window from the ground = 13 ft

Distance of fence from the building = 3 ft

Distance of ladder from the building = (3+8) = 11 ft

We have to find the length of the ladder.

Let the length of the ladder be 'x'

From the diagram we can also say that 'x' is the hypotenuse of the right angled triangle.

Using Pythagoras formula:

⇒ [tex]hypotenuse\ 'x' =\sqrt{(perpendicular)^2+(base)^2}[/tex]

Here base length = 11 ft

Perpendicular = 13 ft

Plugging the values:

⇒ [tex]x=\sqrt{(13)^2+(11)^2}[/tex]

⇒  [tex]x=\sqrt{(169+121)}[/tex]

⇒ [tex]x= \sqrt{290}[/tex]

⇒ [tex]x=17.02[/tex] feet

The length of the ladder = 17 feet to its nearest tenth.

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