A 1.5 mall boy is standing at a distance of 3 m from a 4 m high light post. The light from top of post casts his shadow. What is the length of the boy’s shadow?

Correct option is A

Given:

Height of boy (EB) = 1.5 m

Distance between boy and post (BC) = 3 m

Height of light post (DC) = 4 m

Solution:

Let the length of the shadow = AB m

$$\begin{aligned}&\Rightarrow \tan \mathrm{x}=\frac{E B}{A B}\\&\text { And, In triangle ADC }\\&\Rightarrow \tan \mathrm{x}=\frac{D C}{A C}\end{aligned}$$​​

As both angles are equal 

$$\begin{aligned}& \Rightarrow \frac{E B}{A B}=\frac{D C}{A C} \\& \Rightarrow \frac{1.5}{A B}=\frac{4}{A B+3} \\& \Rightarrow 1.5 \mathrm{AB}+4.5=4 \mathrm{AB} \\& \Rightarrow 2.5 \mathrm{AB}=4.5 \\& \Rightarrow \mathrm{AB}=1.8 \mathrm{~m}\end{aligned}$$​​

Hence, height of the shadow of the boy is 1.8 m.

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