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A drone is flying at a height of $h$ metres. At an instant it observes the angle of elevation of top of an industrial turbine as $60^\circ$ and angle of depression of foot of the turbine as $30^\circ$. If height of turbine is $200$ metres, find the value of $h$ and the distance of drone from the turbine. (Use $\sqrt{3} = 1.73$)
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Let the drone be flying at the height $CD = h$ metres, distance of drone from the turbine be $x$ metres and height of industrial turbine is $AB = 200$ metres
In $\triangle DEB, \tan 30^\circ = \frac{h}{x} \Rightarrow x = h\sqrt{3} \dots (i)$
In $\triangle DEA, \tan 60^\circ = \frac{200-h}{x} \Rightarrow x\sqrt{3} = 200 - h \dots (ii)$
Solving (i) & (ii) we get $x = 50\sqrt{3} = 86.5, h = 50$
$\therefore h = 50$ m and the distance of drone from the turbine is $86.5$ m
Let the drone be flying at the height $CD = h$ metres, distance of drone from the turbine be $x$ metres and height of industrial turbine is $AB = 200$ metres
In $\triangle DEB, \tan 30^\circ = \frac{h}{x} \Rightarrow x = h\sqrt{3} \dots (i)$
In $\triangle DEA, \tan 60^\circ = \frac{200-h}{x} \Rightarrow x\sqrt{3} = 200 - h \dots (ii)$
Solving (i) & (ii) we get $x = 50\sqrt{3} = 86.5, h = 50$
$\therefore h = 50$ m and the distance of drone from the turbine is $86.5$ m