Question

A ladder is leaning against the very top of a building. The base of the ladder is 18 feet from the building and is leaning at a 60 degree angle. How tall is the building?

Answer 1

The height of the building is 18
`√(3)` feet .

Explanation:

Given as :

The distance of the base of ladder from building = d = 18 feet

The ladder is leaning at the angle = Ф = 60°

Let the height of the building = h feet

Now, From figure

Tan angle =
`(\textrm perpendicular)/(\textrm base)`

Or,Tan Ф =
`(\textrm AB)/(\textrm OA)`

Or,Tan 60° =
`(\textrm h)/(\textrm 18)`

Or,
`√(3)` =
`(\textrm h)/(\textrm 18)`

∴ h = 18
`√(3)` feet

So, The height of the building = h = 18
`√(3)` feet

Hence, The height of the building is 18
`√(3)` feet . Answer