Putting this value in ( ), we get = x + , i.e., x = x + x = h = [From ( )] Therefore, the height of the tower is m. Example : The angles of depression of the top and the bottom of an m tall building from the top of a multi-storeyed building are ° and °, respectively. Find the height of the multi- storeyed building and the distance between the two buildings. Solution : In Fig.
. , PC denotes the multi- storyed building and AB denotes the m tall building. We are interested to determine the height of the multi-storeyed building, i.e., PC and the distance between the two buildings, i.e., AC. Look at the figure carefully.
Observe that PB is a transversal to the parallel lines PQ and BD. Therefore, QPB and PBD are alternate angles, and so are equal. So PBD = °. Similarly, PAC = °.
In right PBD, we have Fig. . PD BD = tan ° = or BD = PD In right PAC, we have PC AC = tan ° = PC = AC Also, PC = PD + DC, therefore, PD + DC = AC. Since, AC = BD and DC = AB = m, we get PD + = BD = PD (Why?) This gives PD =