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ICSE Class 10 Answered

The angle of elevation of the bottom of a window 10m above the ground level from a point of the ground is 30 degree.  A pole projecting outwards from the bottom of the window makes an angle of 30 degrees with the wall.  If the angle of elevation of the top of the pole observed from the same point on the ground is 60 degree,  find the length of the pole.
Asked by Pradeep | 13 Jan, 2019, 09:36: AM
answered-by-expert Expert Answer
As shown in figure, angle of elevation of point B, which is bottom of window, is 30°.
If AB = 10m , AB/AC = tan 30 = 1/√3  ; Hence AC = 10√3 m
 
Let BE is the pole projecting from the bottom of the window and makes angle 30° with wall.
Let angle of elevation of tip of the pole E from point C be 60°
 
Perpendicular lines ED and BF are drawn. Let EF = h and BF = x
 
It can be seen from figure, EF/BF = h/x = tan60 = √3   or h = x√3 m ................(1)
 
It can be seen from figure ED/DC = ( x√3+10)/(10√3 - x)  = tan60 = √3 ................(2)
 
by solving eqn.(2) for x, we get x = 10/√3
from eqn.(1), we get h = x√3 = √3 ×(10/√3) = 10 m
 
Pole length = begin mathsize 12px style square root of x squared plus h squared space end root space equals space 20 over 3 square root of 3 space almost equal to space 11.55 space m end style
Answered by Thiyagarajan K | 13 Jan, 2019, 09:21: PM

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