From the top of a house A in a street, the angle of elevation and depression to the top and foot of another house B on the opposite side of the street are 45° and 30° respectively. If the height of house A is 18√3 m, then what is the height of house B?

18(3 + √3) m

AB = house A

PQ = house B

     = PR + RQ

RQ = AB = 18 \(\sqrt {3}\)

tan \(\angle\)AQB   =  AB     :     BQ

                         1      :      \(\sqrt {3}\)

                         ↓               ↓

               18 \(\sqrt {3}\)           18 \(\sqrt {3}\) × \(\sqrt {3}\) = 18 × 3 = 54 m

tan \(\angle\) PAR   = PR     :     AR        (AR = BQ)

                         1      :      1

                         ↓              ↓

                        54            54 (BQ)

Therefore, height of house B = PQ = PR + RQ

                                               = 54 + 18 \(\sqrt {3}\) = 18 (3 + \(\sqrt {3}\)) m