Question

The angles of depression of the top and the bottom of a 8 m tall building from the top of a multi-storeyed building are 30° and 45°, respectively. Find the height of the multi-storeyed building and the distance between the two buildings.

Answer 1

In Fig. , PC denotes the multi-storeyed building and AB denotes the 8 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.
Let PD = x m

So, the height of the multi-storeyed building is {4( √3 + 1) + 8} m = 4(3 + √3) m and the distance between the two buildings is also 4(3 + √3 ) m.