SATHEE: Quantitative Aptitude Ques 2050

Quantitative Aptitude Ques 2050

Question: The angle of elevation of the top of a tower from the bottom of a building is twice that from its top. What is the height of the building, if the height of the tower is 75 m and the angle of elevation of the top of the tower from the bottom of the building is $ 60{}^\circ $ ?

Options:

A) 25 m

B) 37.5 m

C) 50 m

D) 60 m

Show Answer

Answer:

Correct Answer: C

Solution:

We have to find DC. Given, $ 2x=60{}^\circ $

$ \therefore $ $ x=30{}^\circ $ In $ \Delta ABC, $ $ \tan 60{}^\circ =\frac{AB}{BC} $

$ \Rightarrow $ $ \frac{\sqrt{3}}{1}=\frac{75}{BC} $

$ \therefore $ $ BC=\frac{75}{\sqrt{3}}=\frac{75\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}} $ $ =25\sqrt{3}cm $ In $ \Delta AED, $ $ \tan 30{}^\circ =\frac{AE}{ED}=\frac{AE}{25\sqrt{3}} $ $ [\because BC=ED] $

$ \Rightarrow $ $ \frac{1}{\sqrt{3}}=\frac{AE}{25\sqrt{3}} $

$ \therefore $ $ AE=25m $

$ \therefore $ $ DC=EB=AB-AE=75-25=50cm $

Quantitative Aptitude Ques 2049

Quantitative Aptitude Ques 2051

Quantitative Aptitude Ques 2050

Question: The angle of elevation of the top of a tower from the bottom of a building is twice that from its top. What is the height of the building, if the height of the tower is 75 m and the angle of elevation of the top of the tower from the bottom of the building is $ 60{}^\circ $ ?

Options:

Answer:

Solution:

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