Question

The angle of depression of two boats as observers from the masthed of a ship 50m heigh are 45° and 30° respectively. The distance between the two boats if they are on the same side of the masthead is

Answer 1

Let AB and CD be the multi-storeyed building and the building respectively.

 Let  the height of the multi-storeyed building= h m and 

the distance between the two buildings = x m.

 AE = CD = 8 m  [Given]

BE = AB – AE = (h – 8) m 

and 

AC = DE = x m  [Given]

 Also,

 ∠FBD = ∠BDE = 30° (Corresponding angles)

∠FBC = ∠BCA = 45° (Corresponding angles)

 Now,

 In Δ ACB,



 In Δ BDE,



From (i) and (ii), we get,

 

Distance between the two building