Two towers of the same height stand on either side of a read 60 m wide. At a point on the road between the towers, the elevations of the towers are $60^{\circ}$ and $30^{\circ}$ . Find the approximate height of the towers. ___

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Solution

In $Δ A O B$
$\frac{A B}{A O} = \frac{h}{x} = \frac{1}{\sqrt{3}}$

and in $Δ C O D, \frac{C D}{O C} = \frac{h}{(60 - x)} = \sqrt{3} \dots (1)$
for equation (1) and (2)
$\frac{x}{\sqrt{3} (60 - x)} = \sqrt{3} \Rightarrow x = 45 m ∴ h = \frac{45}{\sqrt{3}} = 15 \sqrt{3} = 15 \times 1.732 = 25.98 m$
Hence, the height of the towers is 25.98 m and the distance of the point 'O' from A is 45 m and C is 15 m.

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