A house of height 100 m subtends a right ang | vedclass

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(A) Let the distance between the two houses be $d$. The window is at a height of $64 \ m$. The house of height $100 \ m$ is divided into two parts by

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$48$

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(A) Let the distance between the two houses be $d$. The window is at a height of $64 \ m$. The house of height $100 \ m$ is divided into two parts by the horizontal line from the window: one part of height $64 \ m$ (below the window) and another part of height $(100 - 64) = 36 \ m$ (above the window).Let $	heta$ be the angle that the lower part makes with the horizontal line of distance $d$. Then $	an 	heta = \frac{64}{d}$.The upper part makes an angle $(90^\circ - 	heta)$ with the horizontal line. Then $	an(90^\circ - 	heta) = \frac{36}{d}$,which implies $\cot 	heta = \frac{36}{d}$.Multiplying the two equations: $	an 	heta 	imes \cot 	heta = \frac{64}{d} 	imes \frac{36}{d}$.$1 = \frac{64 	imes 36}{d^2}$.$d^2 = 64 	imes 36$.$d = \sqrt{64 	imes 36} = 8 	imes 6 = 48 \ m$.

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

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