The angle of elevation of the top of a hill f | vedclass

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(B) Let $h$ be the height of the hill and $O$ be the foot of the hill on the horizontal plane.Since the angle of elevation from each vertex $A, B, C$

Vedclass · Accepted Answer

$\frac{a}{2} 	an \alpha \operatorname{cosec} A$

Vedclass · Answer

(B) Let $h$ be the height of the hill and $O$ be the foot of the hill on the horizontal plane.Since the angle of elevation from each vertex $A, B, C$ is $\alpha$,we have $OA = OB = OC = h \cot \alpha$.This implies that $O$ is the circumcentre of $	riangle ABC$ with circumradius $R = h \cot \alpha$.In any triangle $ABC$,the circumradius $R$ is given by $R = \frac{a}{2 \sin A}$.Equating the two expressions for $R$: $h \cot \alpha = \frac{a}{2 \sin A}$.Therefore,$h = \frac{a 	an \alpha}{2 \sin A} = \frac{a}{2} 	an \alpha \operatorname{cosec} A$.

The angle of elevation of the top of a hill from each of the vertices $A, B, C$ of a horizontal triangle is $\alpha$. The height of the hill is

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