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
Solution(By Examveda Team)
Let AB is girls and CD is lamp-post AB = 1.5which casts her shadow EB
$$\eqalign{ & \therefore EB = 4.5\,m,\,BD = 3\,m \cr & {\text{Now in }}\Delta AEB \cr & \tan \theta = \frac{{AB}}{{BE}} = \frac{{1.5}}{{4.5}} = \frac{1}{3} \cr & {\text{and in }}\Delta CED \cr & \tan \theta = \frac{{CD}}{{ED}} \Rightarrow \frac{1}{3} = \frac{h}{{4.5 + 3}} \cr & \Rightarrow \frac{1}{3} = \frac{h}{{7.5}} \cr & \Rightarrow h = \frac{{7.5}}{3} - 2.5\,m \cr & \therefore {\text{Height of lamp - post}} = {\text{2}}{\text{.5}}\,m \cr} $$
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