A flag-staff of 5 , m high stands on a buildi | vedclass

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(B) Let the observer be at point $O$ at a height of $30 \, m$ from the ground. The building height is $25 \, m$ and the flag-staff is $5 \, m$ on top

Vedclass · Accepted Answer

$5\sqrt{\frac{3}{2}}$

Vedclass · Answer

(B) Let the observer be at point $O$ at a height of $30 \, m$ from the ground. The building height is $25 \, m$ and the flag-staff is $5 \, m$ on top of it,so the total height is $30 \, m$. Let the horizontal distance between the observer and the building be $x$. The observer is at the same level as the top of the flag-staff. Let the angle subtended by the flag-staff at the observer be $\alpha$. Let the angle subtended by the building at the observer be $\alpha$. From the geometry,$	an \alpha = \frac{5}{x}$ and $	an 2\alpha = \frac{30}{x}$. Using the identity $	an 2\alpha = \frac{2	an \alpha}{1 - 	an^2 \alpha}$,we have: $\frac{30}{x} = \frac{2(5/x)}{1 - (5/x)^2} = \frac{10/x}{(x^2 - 25)/x^2} = \frac{10x}{x^2 - 25}$. $30(x^2 - 25) = 10x^2$ $\Rightarrow 3x^2 - 75 = x^2$ $\Rightarrow 2x^2 = 75$ $\Rightarrow x^2 = \frac{75}{2}$ $\Rightarrow x = \sqrt{\frac{75}{2}} = 5\sqrt{\frac{3}{2}}$. The distance of the observer from the top of the flag-staff is the horizontal distance $x$ because the observer and the top of the flag-staff are at the same height $(30 \, m)$. Thus,the distance is $5\sqrt{\frac{3}{2}} \, m$.

$A$ flag-staff of $5 \, m$ high stands on a building of $25 \, m$ high. An observer is at a height of $30 \, m$. The flag-staff and the building subtend equal angles at the observer. The distance of the observer from the top of the flag-staff is

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