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34 votes
The base of a ladder shouldbe placed 3 feet from thewall for every 5 feet ofladder length.How long a ladder is neededto safely reach 36 feetabove the ground?

The base of a ladder shouldbe placed 3 feet from thewall for every 5 feet ofladder-example-1
User Lamp
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1 Answer

22 votes
22 votes

Using trigonometry, we can find the answer as follows:

let θ be the angle indicated in the figure above, then:

cos θ = 3/5


\theta=\cos^(-1)((3)/(5))=0.927\text{ rad}

Then, let L be the length of the ladder that is needed to reach 36 feet above the ground, then:

sin θ = 36/L

solving for L:

L = 36/sin θ

Using the value of θ found above, we obtain: sin θ = 0.8

L = 36/0.8 = 45 ft

So 45 ft is the length of the ladder that is needed to reach 36 feet above the ground.

The base of a ladder shouldbe placed 3 feet from thewall for every 5 feet ofladder-example-1
User KevinOelen
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