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

Answer: Option C

Let AB is girls and CD is lamp-post AB = 1.5
which casts her shadow EB

$$\begin{array}{rl}& \therefore EB=4.5m,BD=3m\\ & \text{Now in }\Delta AEB\\ & \tan \theta =\frac{AB}{BE}=\frac{1.5}{4.5}=\frac{1}{3}\\ & \text{and in }\Delta CED\\ & \tan \theta =\frac{CD}{ED}\Rightarrow \frac{1}{3}=\frac{h}{4.5+3}\\ & \Rightarrow \frac{1}{3}=\frac{h}{7.5}\\ & \Rightarrow h=\frac{7.5}{3}-2.5m\\ & \therefore \text{Height of lamp - post}=\text{2}\text{.5}m\end{array}$$