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A statue 3 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is $60^\circ$ and from the same point the angle of elevation of the top of the pedestal is $30^\circ$. Find the height of the pedestal and its distance from the point of observation on ground. (Use $\sqrt{3} = 1.73$)
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Solution: Let height of the pedestal be $AB = h$ m and the distance between pedestal and the point of observation on the ground be $AD = x$ m and the height of the statue be BC.
In $\Delta DAB, \tan 30^\circ = \frac{h}{x} \Rightarrow x = h\sqrt{3}$
In $\Delta DAC, \tan 60^\circ = \frac{h+3}{x} \Rightarrow 2h = 3$
Solving equations to get $h = 1.5$ and $x = 2.6$
The height of the pedestal = 1.5 m and distance from the point of observation = 2.6 m
In $\Delta DAB, \tan 30^\circ = \frac{h}{x} \Rightarrow x = h\sqrt{3}$
In $\Delta DAC, \tan 60^\circ = \frac{h+3}{x} \Rightarrow 2h = 3$
Solving equations to get $h = 1.5$ and $x = 2.6$
The height of the pedestal = 1.5 m and distance from the point of observation = 2.6 m