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

Answer:

The height of the building is 18$\sqrt{3}$ feet .

Step-by-step 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 = $\dfrac{\textrm perpendicular}{\textrm base}$

Or,Tan Ф = $\dfrac{\textrm AB}{\textrm OA}$

Or,Tan 60° = $\dfrac{\textrm h}{\textrm 18}$

Or, $\sqrt{3}$ = $\dfrac{\textrm h}{\textrm 18}$

∴ h = 18$\sqrt{3}$ feet

So, The height of the building = h = 18$\sqrt{3}$ feet

Hence, The height of the building is 18$\sqrt{3}$ feet . Answer