Q.19. An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is $45°$. What is the height of the chimney.

Dear Student,


Consider a AB standing at a distance of CE from chimney. Let height of the chimney be CD.

So we found that AE // BC and AE = BC = 28.5 m

Also AB // CE and AB = CE = 1.5 m

To find : CD

In triangle DAE
$$\begin{gathered} \tan 45°=\frac{\mathrm{DE}}{\mathrm{AE}} \\ \Rightarrow 1=\frac{\mathrm{DE}}{\mathrm{AE}} \\ \Rightarrow \mathrm{DE}=\mathrm{AE}=28.5 \mathrm{m} \end{gathered}$$
 

Therefore height of the Chimney = DE + CE = 28.5 + 1.5 = 30 m

Regards