# If a 1.5 m tall girl stands at a distance of 3 m from a lamp-post and casts a shadow of length 4.5 m on the ground, then the height of the lamp-post is

A. 1.5 m B. 2 m C. 2.5 m D. 2.8 m Answer: Option C
Let AB is girls and CD is lamp-post AB = 1.5 which casts her shadow EB $\begin{array}{l}\therefore\text{EB}=4.5\ \text{m, BD}=3\text{m}\\ \text{Now in }\triangle\text{AEB}\\ \tan\theta=\frac{AB}{BE}=\frac{1.5}{4.5}=\frac{1}{3}\\ \text{and in }\triangle\text{CED}\\ \tan\theta=\frac{CD}{ED}\Rightarrow\frac{1}{3}=\frac{h}{4.5+3}\\ \Rightarrow\frac{1}{3}=\frac{h}{7.5}\\ \Rightarrow h=\frac{7.5}{3}=2.5\mathrm{~m}\\ \therefore\text{Height of lamp post}\\ =2.5\text{ m}\end{array}$