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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.
Solution
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
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