ICSE Class 10 Answered
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 | 04 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 h 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 | 04 Apr, 2013, 11:20: PM
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