Question

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?

Answer 1

Using trigonometry, we can find the answer as follows:

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

cos θ = 3/5

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

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.