Question

From a window ( h metres high above the ground) of a house in a street, angle of elevation and depression of the top and the bottom of an other house on the opposite side of the street are theta and alpha respt. Show that the height of the opposite house is h(1+tan theta cot alpha)

Answer 1

Let B be the position of the window above the ground. AB = h m (Given)

Let the height of the opposite house, CD = x m

Given, ∠DBE = θ and ∠EBC = α

CE = AB = h m

DE = CD – CE = (x – h) m

In ΔDBE,



In ΔBEC,



From (1) and (2), we get



Thus, the height of the opposite house is h (1 + tan θ cot α).
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Answer 2

$\textbf{Answer is in Attachment ! }$