Answer to Question #321572 in Trigonometry for noone

Question #321572

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


1
Expert's answer
2022-06-10T11:50:03-0400

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

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




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

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


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





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

So LO=POtanL=4.5mtan20°=4.5m0.3639=12.37mLO=\frac{PO}{\tan L}=\frac{4.5\,m}{\tan20\degree}=\frac{4.5\,m}{0.3639}=12.37\,m.


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