Question

A 1.5-m-tall boy stands at a distance of 3 m from a lamp post and casts a shadow of 4.5 m on the ground. Find the height of the lamp post.

Answer 1

Let $AB$ be the lamppost, $CD$ be the boy and $CE$ be the shadow of $CD$.
Also, let ∠$AEB\hspace{0.17em}=\theta$ and the height of the lamppost be h.



From the right ∆​$ECD$, we have:
$\tan \theta =\frac{CD}{CE}=\frac{1.5}{4.5}=\frac{1}{3}$

Now, from the right ∆$EAB$, we have:
$\frac{AB}{AE}=\tan \theta =\frac{1}{3}$ [∵ $\tan \theta =\frac{1}{3}$]

⇒ $\frac{h}{(AC+CE)}=\frac{h}{(4.5+3)}=\frac{1}{3}$

⇒ $h=\frac{7.5}{3}=2.5$ m

∴ Height of the lamppost = $AB=h=2.5$ m