Question
Fri November 09, 2012 By:
 

From an aeroplane vertically above a straight horizantal plane the angles of depression of two consecutive kilometre stones on opposite sides of the planesare found to be alpha and beta show that the height of the aeroplane is 1/cot alpha +cot beta ? plzzz reply fast

Expert Reply
Fri November 09, 2012
Imagine a point A directly below the aeroplane on the ground.
Let the distance of the point A from each of stones is x and y.
Then x+y =1 since these are consecutive stones.
 
Let us say the height of aeroplane is h.
 
So, x/h= cotc   so, x=hcot?  
and y/h = cot?  so y=hcot?
 
adding the above two we get,
 
so x+y = h(cot? + cot?) = 1
hence  h = 1/(cot? + cot?) 
 
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