Question

The angles of depression of the top and the bottom of a 10 m tall building from the top of a multi-storeyed building are 30° and 45°, respectively. Find the height of the multi-storeyed building.

Options

• 5 m

• `5 (sqrt3 + 3)` m

• 15 m

• 10 m

Answer 1

`5 (sqrt3 + 3)  "m"` 

Explanation:

The above figure represents the situation apply

`angle "CBE" = angle "BEF"` and `angle "DAE" = angle "AEF"`   (alternate angles)

`"tan" (angle "EAD") = "tan"  45^circ = "ED"/"AD" = ("EC + CD")/"AD"`

`=> "AD" xx "tan"  45^circ = "EC + CD"` .....(1)

and tan `(angle "EBC") = "tan"  30^circ = "EC"/"CB"`

`=> "CB" xx "tan"  30^circ = "EC"` .....(2)

Subtracting eq (2) from (1)

`=> "AD" xx "tan"  45^circ - "CB" xx "tan"  30^circ = "CD"`

`=> "AD" ("tan"  45^circ - "tan"  30^circ) = "CD"       (because "AD = CB")`

`=> "AD" (1 - 1/sqrt3) = 10`

`=> "AD" = 5 (3 + sqrt3)  "m"`

`=> "ED" = "AD" ("tan" 45^circ = 1) `