two persons are 'a'm apart and the height of one is dooublethat of the other. If from the middle point of the line joining their feet, an observer finds the angular elevation of their tops to be complementary, then the height of the shorter person is:

Asked by sowmya subathra | 4th Apr, 2013, 06:44: AM

Expert Answer:

Answer : Given : two persons are 'a'm apart and the height of one is dooublethat of the other. If from the middle point of the line joining their feet, an observer finds the angular elevation of their tops to be complementary
To find :  the height of the shorter person 
 

 

Let AB = a m be the line joining the feet of the persons and C be the mid-point of this line.

Thus, AC = CB = a/ 2 m

Also, let be the height of the of the shorter person then the height of the taller person will be 2h.

 

Now from the figure, we have

tan x = h /(a/2) = 2h /a ..........................(1)        { tan = P/H }
 
also
tan(90-x) = 2h / (a/2)   =4h/a
cot x = 4h/a .......................(2)
 
multiply eq 1 by eq 2
=> tan x cotx = (2h/a) (4h/a)
=> 8h2 / a2 = 1
=> 8h2 = a2 
=> h2 = a2 /8
=> h = a / (2 3/2) Answer 

Answered by  | 4th Apr, 2013, 11:20: PM

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