Question

A PLANE IS AT A VERTICAL HEIGHT OF H. THE ANGELS OF DEPRESSION OF TWO TANKS ON THE HORIZONTAL GROUND ARE FOUND TO HAVE MASURE α AND β (α>β) .PROVE THAT THE DISTANCE BETWEEN THE TANK IS h(tanα-tanβ)/tanα*tanβ


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Answer 1

x=H ( (tan(a) - tan(b)) / tan(a)tan(b) )

-Let me consider the angle of depressions as a and b in place of alpha and beta,

(refer the picture along with this derivation)

-We need to find x, which is the distance between two tanks at r and s

-From triangle pqr,

we have tan(a) = H/y

=> y = H/tan(a).............1

-From triangle pqs,

we have tan(b) = H/(x+y)

=> y = H/tan(b)  -  x ........................2

-From equations 1 and 2, equating the y's,

we have

H/tan(a) = H/tan(b)  -  x

-On simplifying, for x,

we get x=H ( (tan(a) - tan(b)) / tan(a)tan(b) )