Question

A flag post was erected on the top of a building. If vertical angle subtended at bottom and top of the flag post are $8^{\circ }$ and $9^{\circ }$ respectively, then the height of the flag post is ? [Assume R.L of top and bottom of building to be 184.4 m and 145.2 m respectively, height of instrument to be 1.2 m and width of the building is very less as compared to the distance to the building from the theodolite]

• A. 4.825 m
• B. 3.658 m
• C. 4.165 m
• D. 4.447 m

Answer 1

The correct option is A 4.825 m

Height of building above instrument,

H = (184.4 - 145.2) -1.2

= 38 m

$\tan 8^{\circ }=\frac{H}{D}$

$\Rightarrow D=\frac{H}{\tan 8^{\circ }}....\left(i\right)$

$\tan 9^{\circ }=\frac{H+h}{D}....\left(ii\right)$

From (i) and (ii),

$\Rightarrow \tan 9^{\circ }=\frac{H+h}{H}\tan 8^{\circ }$

$\therefore h=4.825m$