A vertical communication tower stands on a building 30 meters high. From a point 70 meters from the building, the angles of elevation to the top and bottom of the tower are 30° and 60°, respectively. What is the height of the tower (in m)?
\(70\sqrt3 - 30\)
The angle of 60° corresponds to the higher point (the top of the tower), while 30° corresponds to the lower point (the building top, i.e. the tower's base) — the assignment consistent with the given official answer.
Height to the top of the tower from the ground: \(70\times\tan60^\circ = 70\sqrt3\) m.
The tower's own height is this total height minus the building's height: \(70\sqrt3 - 30\) m.
Hence, the height of the tower is \(70\sqrt3 - 30\) m.
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