Question

paul is standing at the top of an escalator and lily is standing at the bottom. Their vertical distance is 4.5 m and the angle of elevation of paul from lily is 20 degrees. Find the horizontal distance between them

Answer 1

Let Paul is standing at point P, Lily is standing at point L.

Construct a right triangle $\triangle POL$ ($\angle O = 90\degree$):

Vertical distance of the escalator 4.5 m, so $PO=4.5\,m$.

The angle of elevation is 20 degrees, so $\angle L=20\degree$.

You need to find the horizontally distance between them, so You need to find $LO$.

Using the trigonometric properties of the acute angle of a right triangle we have: $\tan L=\frac{PO}{LO}$.

So $LO=\frac{PO}{\tan L}=\frac{4.5\,m}{\tan20\degree}=\frac{4.5\,m}{0.3639}=12.37\,m$.