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A statue, $2$ 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 bottom of the statue is $45^\circ$. Find the height of the pedestal and its distance from the point of observation on the ground. (use $\sqrt{3} = 1.73$)
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Solution: For correct figure: (1)
Let AB be the pedestal
In $\triangle CAD$, $\tan 60^\circ = \frac{h+2}{x}$ (1)
$\Rightarrow h = \sqrt{3} x - 2$ ...... (i) (
frac{1}{2})
In $\triangle BAD$, $\tan 45^\circ = \frac{h}{x}$ (1)
$\Rightarrow h = x$ ...... (ii) (
frac{1}{2})
Solving and getting, $x = h = \frac{2}{\sqrt{3}-1}$ (
frac{1}{2})
$x = 2.73$ m and $h = 2.73$ m (
frac{1}{2})
Let AB be the pedestal
In $\triangle CAD$, $\tan 60^\circ = \frac{h+2}{x}$ (1)
$\Rightarrow h = \sqrt{3} x - 2$ ...... (i) (
frac{1}{2})
In $\triangle BAD$, $\tan 45^\circ = \frac{h}{x}$ (1)
$\Rightarrow h = x$ ...... (ii) (
frac{1}{2})
Solving and getting, $x = h = \frac{2}{\sqrt{3}-1}$ (
frac{1}{2})
$x = 2.73$ m and $h = 2.73$ m (
frac{1}{2})