waecmaths question:
The angle of elevation of the top of a tree from a point 27m away and on the same horizontal ground as the foot on the tree is 30o. Find the height of the tree.
Option A:
27m
Option B:
$13.5\sqrt{3}m$
Option C:
$13.5\sqrt{2}m$
Option D:
$9\sqrt{3}m$
waecmaths solution:
$\begin{align} & \text{Let }BC\text{ be the height of the tree} \\ & \tan 30{}^\circ =\frac{BC}{AB} \\ & \tan 30{}^\circ \times AB=BC \\ & \frac{1}{\sqrt{3}}\times 27m=h \\ & \frac{\sqrt{3}}{\sqrt{3}\times \sqrt{3}}\times 27m=h \\ & \frac{\sqrt{3}}{3}\times 27m=h \\ & h=9\sqrt{3}m \\\end{align}$
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