First slide

Applications of trigonometry

Question

A bird is sitting on the top of a vertical pole 20m high and its elevation from a point O on the ground is 45⁰. It flies off horizontally straight away from the point O. After one second, the elevation of bird from O is reduced to 30⁰, then the speed (in m/s), of the bird is

Moderate

Solution

$Let AB = height of vertical pole = 20$
$From ΔOAB, \tan 45^{\circ} = \frac{AB}{OA}$
$\Rightarrow OA = AB = 20$
$\begin{aligned} Let C be the new position of bird \\ Let BC = x \end{aligned}$
$From ΔOCD, \tan 30^{\circ} = \frac{20}{x + 20}$
$\Rightarrow x = 20 (\sqrt{3} - 1) = 14.64 m / s$

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