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# As observed from the top of a lighthouse 100m above sea level the angle of depression of a ship sailing directly towards it changes from 30 degree to 60 degree. determine the distance travelled by the ship during the period of observation

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An important and exam oriented question from trigonometry as it was already asked in previous year paper of 2004 and 2008 in which we have to find the distance travelled by the ship during the period of observation when observed from the top of a lighthouse 100m above sea level the angle of depression of a ship sailing directly towards it changes from 30 degree to 60 degree.

RS Aggarwal, Class 10, Chapter 14, question no 27.

Topic Height and Distance.

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1. ## The height of tower isÂ 100m

The angle of depression (initial)Â =30âˆ˜
The distance from tower isÂ tan30Â°=distanceâ€‹/height
1/âˆš3=Distanceâ€‹/100
Distance=100â€‹/âˆš3m

The angle of depression (final)Â =45âˆ˜
The distance from tower isÂ tan45=distance/heightâ€‹1=Distance/100
â€‹Distance=100m

The distacne covered = 100âˆ’100/âˆš3â€‹Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â =100âˆ’57.73
Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â =42.27m

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