Lucia needs to buy a ladder to reach her roof. The edge of the roof is 21.125 feet high. To use a ladder safely, the base of a ladder should be 1 foot away from a building for every 3.25 feet of building height. The ladder should extend 3 feet longer than the edge of the roof. How long does the ladder need to be? Round your answer to the nearest tent

Answers

Answer 1

Answer:

The length of the ladder is 25.1ft

Step-by-step explanation:

We are given

Height of the building  = 21.125ft = a (let)

On forming a triangle we have the height of the building as 'a'

It says that the base of a ladder should be 1 foot away from a building for every 3.25 feet of building height.

so for 21.125ft of height of building  = 21.125/3.5 = 6.5ft

we need the base of the ladder to be at 6.5ft  away from the building on the ground.

Let 6.5ft = b

Now we have the height of the building 'a' and the base distance of the ladder from the building 'b'

Applying Pythagoreans theorem

[tex]\sqrt{a^2 + b^2} =c^2[/tex]  where c represents the ladder length

on substituting the values of a and b

we get c= 22.1ft

but the ladder is 3ft longer than the edge of the roof

so final length of the ladder = 22.1 +3 = 25.1ft


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