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Two pillars of equal heights stand on either side of a roadway $150$ m wide. From a point on the roadway between the pillars, the angles of elevation of the top of the pillars are $60^\circ$ and $30^\circ$ respectively. Find the height of the pillars and the position of the point from the pillars.
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OR
(b)
In $\triangle PDC$
$\frac{h}{x} = \tan 30^\circ$
$x = \sqrt{3}h$ ............(i) (1 Mark)
In $\triangle PBA$
$\frac{h}{150-x} = \tan 60^\circ$
$h = (150 – x) \sqrt{3}$ ........(ii) (1.5 Mark)
Solving equations (i) and (ii)
$h =37.5 (\sqrt{3})$ m or $64.875$ m (1 Mark)
$x = 112.5$ m, $150 – x = 37.5$ m (1.5 Mark)
(b)
In $\triangle PDC$
$\frac{h}{x} = \tan 30^\circ$
$x = \sqrt{3}h$ ............(i) (1 Mark)
In $\triangle PBA$
$\frac{h}{150-x} = \tan 60^\circ$
$h = (150 – x) \sqrt{3}$ ........(ii) (1.5 Mark)
Solving equations (i) and (ii)
$h =37.5 (\sqrt{3})$ m or $64.875$ m (1 Mark)
$x = 112.5$ m, $150 – x = 37.5$ m (1.5 Mark)