From the top of a building 20 m high, the angles of depression of the top and the bottom of a tower standing on the same horizontal ground are observed to be 30° and 60°, respectively. The height (in meter) of the tower is: (Round off your answer to two decimal places.)
13.33 m
Let the tower's height be h and the horizontal distance be d.
Depression to the tower's bottom is 60°: \(\tan60^\circ = \dfrac{20}{d} \Rightarrow d = \dfrac{20}{\sqrt3}\).
Depression to the tower's top is 30°: the vertical gap between the building top and tower top is \(20-h\), so \(\tan30^\circ = \dfrac{20-h}{d}\).
\(20-h = \dfrac{d}{\sqrt3} = \dfrac{20/\sqrt3}{\sqrt3} = \dfrac{20}{3}\).
\(h = 20-\dfrac{20}{3} = \dfrac{40}{3} \approx 13.33\).
Hence, the height of the tower is approximately 13.33 m.
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