ItsTri-gono-metry
Geometry
Level
pending
If the angles of elevation of a tower from two points distant "a" and "b" (a>b) from its foot and in the same straight line from it are 30 degree and 60 degree , then the height of the tower is ?
\sqrt{a/b}
\sqrt{a-b}
\sqrt{a+b}
\sqrt{ab}
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1 solution
let the height be h. then tan30 = h/a . =>1/ \sqrt(3) = h/a. => a = h \sqrt(3). similarly , tan 60 = h/b => \sqrt(3) = h/b => b = h/ \sqrt(3). now a*b = h/ \sqrt(3) * h \sqrt(3). = h^2. therefore h = \sqrt(ab).