SATHEE: Quantitative Aptitude Ques 179

Quantitative Aptitude Ques 179

Question: The angles of elevation of the top of a building from the top and bottom of a tree are x and y. respectively. If the height of the tree is h m, then the height of the building (in metre) is

Options:

A) $ \frac{h\cot x}{\cos x+\cot y} $

B) $ \frac{h\cot ,y}{\cos x+\cot y} $

C) $ \frac{h\cot ,x}{\cot x-\cot y} $

D) $ \frac{h\cot ,y}{\cot x-\cot y} $

Show Answer

Answer:

Correct Answer: C

Solution:

Let height of tree be h m and height of building be b m. In $ \Delta AED, $ $ \tan x=\frac{AE}{ED} $

$ \Rightarrow $ $ \tan x=\frac{b-h}{ED} $

$ \Rightarrow $ $ ED=(b-h)\cot x $ (i) From $ \Delta ABC, $ $ \tan y=\frac{AB}{BC} $

$ \Rightarrow $ $ \tan y=\frac{b}{BC} $

$ \Rightarrow $ $ BC=b\cot y $ (ii) From Eqs. (i) and (ii), we get $ BC=ED $

$ \therefore $ $ (b-h)\cot x=b\cot y $

$ \Rightarrow $ $ b\cot x-h\cot x=b\cot y $

$ \Rightarrow $ $ b,(\cot x-\cot y)=h\cot x $

$ \therefore $ $ b=\frac{h\cot x}{\cot x-\cot y} $

Quantitative Aptitude Ques 178

Quantitative Aptitude Ques 180

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