JAMB 1987 · UME · Q40✱✱

Elevation, depression & bearings

From two points $X$ and $Y$ , 8 m apart and in line with a pole, the angles of elevation of the top of the pole are $30^\circ$ and $60^\circ$ respectively. Find the height of the pole, assuming that $X$ , $Y$ and the foot of the pole are on the same horizontal plane.

Worked solution (try it first)

Let the height be $h$ .
$Y$ has the larger angle, so it is nearer: its distance to the foot is $\frac{h}{\tan60^\circ} = \frac{h}{\sqrt3}$ .
From $X$ the distance is $\frac{h}{\tan30^\circ} = \sqrt3\,h$ .
The two distances differ by 8 m: $\sqrt3\,h - \frac{h}{\sqrt3} = 8$ , so $\frac{2h}{\sqrt3} = 8$ .
So $h = 4\sqrt3$ m, option C.

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