A house of height $ 100 \mathrm{~m} $ subtends a right angle at the window of an opposite house. If the height of the window be $ 64 \mathrm{~m} $, then the distance between the two houses is

Question

A house of height $ 100 \mathrm{~m} $ subtends a right angle at the window of an opposite house. If the height of the window be $ 64 \mathrm{~m} $, then the distance between the two houses is, $ 48 \mathrm{~m} $, $ 36 \mathrm{~m} $, $ 54 \mathrm{~m} $, $ 72 \mathrm{~m} $

MARKS App · Accepted Answer

In ∆ D A B , tan θ = 64 d ⇒ d = 64 cot θ 1 In ∆ C D E , tan 90 ° - θ = 100 - 64 d ⇒ d = 36 tan θ … 2 From Equations 1 and 2 , we get d 2 = 36 × 64 ⇒ d = 48 m

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