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Two poles of equal heights are standing opposite each other on either side of the road which is $85$ m wide. From a point between them on the road, the angles of elevation of the top of the poles are $60^\circ$ and $30^\circ$ respectively. Find the height of the poles and the distances of the point from the poles. (Use $\sqrt{3} = 1.73$)
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In $\Delta BAE, \tan 30^\circ = \frac{h}{85 - x} \Rightarrow 85-x = h\sqrt{3}$ (i)
In $\Delta DCE, \tan 60^\circ = \frac{h}{x} \Rightarrow h = x\sqrt{3}$ (ii)
Using (i) & (ii) $x = 21.25, 85 - x = 63.75$ and $h = 36.76$
Height $= 36.76$ m, distances are $21.25$ m and $63.75$ m
In $\Delta BAE, \tan 30^\circ = \frac{h}{85 - x} \Rightarrow 85-x = h\sqrt{3}$ (i)
In $\Delta DCE, \tan 60^\circ = \frac{h}{x} \Rightarrow h = x\sqrt{3}$ (ii)
Using (i) & (ii) $x = 21.25, 85 - x = 63.75$ and $h = 36.76$
Height $= 36.76$ m, distances are $21.25$ m and $63.75$ m