From the top of a hill h metres high, the ang | vedclass

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Question

(A) Let $AB$ be a hill of height $h$ and $CD$ be a pillar of height $h^{\prime}$.Let $E$ be a point on $AB$ such that $ED$ is horizontal.In $	riangle

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$\frac{h(	an \beta-	an \alpha)}{	an \beta}$

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(A) Let $AB$ be a hill of height $h$ and $CD$ be a pillar of height $h^{\prime}$.Let $E$ be a point on $AB$ such that $ED$ is horizontal.In $	riangle EBD$, $	an \alpha = \frac{BE}{ED} = \frac{h-h^{\prime}}{ED}$, so $ED = \frac{h-h^{\prime}}{	an \alpha}$.In $	riangle ABC$, $	an \beta = \frac{AB}{AC} = \frac{h}{ED}$, so $ED = \frac{h}{	an \beta}$.Equating the two expressions for $ED$:$\frac{h-h^{\prime}}{	an \alpha} = \frac{h}{	an \beta}$$h-h^{\prime} = \frac{h 	an \alpha}{	an \beta}$$h^{\prime} = h - \frac{h 	an \alpha}{	an \beta} = h \left(1 - \frac{	an \alpha}{	an \beta}ight) = \frac{h(	an \beta - 	an \alpha)}{	an \beta}$.

From the top of a hill $h$ metres high, the angles of depression of the top and the bottom of a pillar are $\alpha$ and $\beta$ respectively. The height (in metres) of the pillar is

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