A house of height 100 m subtends a right angle at the window of an opposite house. If the height of the window be 64 m, the distance between the two houses is:

A) 48 m

B) 36 m

C) 54 m

D) 72 m

Correct answer:
A) 48 m

Description for Correct answer:
In \( \Large \triangle DAB, \tan \theta = \frac{64}{d} \)



\( \Large d = 64 \cot \theta \) ...(i)

In \( \Large \triangle CDE, \tan \left(90 ^{\circ} - \theta \right) = \frac{ \left(100 - 64\right) }{d} \)

\( \Large d = 36 \tan \theta \) ...(ii)

From Eqs. (i) and (ii), we get

\( \Large d^{2} = 36 \times 64 => d = 48 m\)

Please provide the error details in above question

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