A house subtends a right angle at the window of the opposite house and the angle of elevation of the window from the bottom of the first house is $60$. If the distance between the two houses be $6$m, then the height of the first house is?

Let the height of the first house be H. The window is at height h. From the bottom of the first house, the angle of elevation to the window is 60 degrees, so tan(60) = h/6, meaning h = 6 * sqrt(3). The house subtends 90 degrees at the window, implying the height of the house above the window is 6 * tan(30) = 6 * (1/sqrt(3)) = 2 * sqrt(3). Total height = 6 * sqrt(3) + 2 * sqrt(3) = 8 * sqrt(3) m.