Question

In the figure given, from the top of a building AB = 60 m high, the angles of depression of the top and bottom of a vertical lamp post CD are observed to 30o and 60o respectively. Find:

1) The horizontal distance between AB and CD.

2) The height of the lamp post.

Answer 1

1) In ΔABC

`tan 60^@ = (AB)/(BC)`

`=> sqrt3 = 60/"BC"`

`=> BC = 60/sqrt3 = 60/sqrt3 xx sqrt3/sqrt3 = 20sqrt3 = 20 xx 1.732` = 34.64 m

2) Since BEDC is a rectangle,

`ED = BC = 20sqrt3` m

In ΔAED,

`tan 30^@ = "AE"/"ED"`

`=> 1/sqrt3 = "AE"/(20sqrt3)`

`=> AE = 20 m`

∴ Height of the lamp post = BE = AB - AE = 60 - 20 = 40 m