Q. 95.0( 1 Vote )


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Answer :


https://gs-post-images.grdp.co/user_files/63094/15047/images/extra-9_files/Image21.gif

Given:

Height of the flagstaff, h = 7 m

Angle of elevation of the bottom of flagstaff, θ = 30°

Angle of elevation of top of flag staff, ϕ = 45 °

To find: Height of the tower

Solution:


Let BC be the height of the tower and DC be the height of the flag-staff.


In right angle Δ ABC,


AB = BC cot 30°


AB = BC
× √ 3 …………………. (i)


In right angled Δ ABD,


AB = BD cot 45°


AB = (BC + CD) cot 45°


AB = (BC + 7) …………………. (ii)


Equating (i) and (ii)


(BC + 7) = BC
× √3


BC(
√3 - 1) = 7


BC = 7/0.73

= 9.58 m


Therefore the height of the tower is 9.58 m.

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