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 CShow Answer
Solution(By Apex Team)
Let AB is girls and CD is lamp-post AB = 1.5
which casts her shadow EB
$\begin{array}{l}\therefore\text{EB}=4.5\ \text{m, BD}=3\text{m}\\
\text{Now in }\triangle\text{AEB}\\
\tan\theta=\frac{AB}{BE}=\frac{1.5}{4.5}=\frac{1}{3}\\
\text{and in }\triangle\text{CED}\\
\tan\theta=\frac{CD}{ED}\Rightarrow\frac{1}{3}=\frac{h}{4.5+3}\\
\Rightarrow\frac{1}{3}=\frac{h}{7.5}\\
\Rightarrow h=\frac{7.5}{3}=2.5\mathrm{~m}\\
\therefore\text{Height of lamp post}\\
=2.5\text{ m}\end{array}$
$\begin{array}{l}\therefore\text{EB}=4.5\ \text{m, BD}=3\text{m}\\
\text{Now in }\triangle\text{AEB}\\
\tan\theta=\frac{AB}{BE}=\frac{1.5}{4.5}=\frac{1}{3}\\
\text{and in }\triangle\text{CED}\\
\tan\theta=\frac{CD}{ED}\Rightarrow\frac{1}{3}=\frac{h}{4.5+3}\\
\Rightarrow\frac{1}{3}=\frac{h}{7.5}\\
\Rightarrow h=\frac{7.5}{3}=2.5\mathrm{~m}\\
\therefore\text{Height of lamp post}\\
=2.5\text{ m}\end{array}$
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