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From a point on the ground, the angle of elevation of the top of a pedestal is $30^\circ$ and that of the top of the flagstaff fixed on the pedestal is $60^\circ$. If the length of the flagstaff is $5$ m, then 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: Correct figure [1 mark]
Let $AB$ be the pedestal of height $h$ and distance from the point of observation on ground be $x$.
In $\Delta ABC, \tan 30^\circ = \frac{h}{x} \Rightarrow x = h\sqrt{3}$ ..........(i) [1 1/2 marks]
In $\Delta DBC, \tan 60^\circ = \frac{h + 5}{x} \Rightarrow h + 5 = x\sqrt{3}$ ..........(ii) [1 1/2 marks]
Using (i) & (ii) $h = 2.5$ and $x = 4.33$ [1/2 + 1/2 mark]
$\therefore$ The height of the pedestal is $2.5$ m and its distance from the point of observation is $4.33$m.
Let $AB$ be the pedestal of height $h$ and distance from the point of observation on ground be $x$.
In $\Delta ABC, \tan 30^\circ = \frac{h}{x} \Rightarrow x = h\sqrt{3}$ ..........(i) [1 1/2 marks]
In $\Delta DBC, \tan 60^\circ = \frac{h + 5}{x} \Rightarrow h + 5 = x\sqrt{3}$ ..........(ii) [1 1/2 marks]
Using (i) & (ii) $h = 2.5$ and $x = 4.33$ [1/2 + 1/2 mark]
$\therefore$ The height of the pedestal is $2.5$ m and its distance from the point of observation is $4.33$m.