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Question
From the top of the tower h metre high , the angles of depression of two objects , which are in the line with the foot of the tower are ∝ and ß (ß> ∝ ) cts .
Solution
Let the two objects be at points C and D.
The angle of depression for the point C is `ßß` and for the point D is `∝∝`
In ∆ABC,
`tan ß=h/(BC)`
`⇒ BC= h /tanß `
`⇒ tan∝= h/( BC+CD)`
`⇒∝= h/(h/tanß+CD)`
`⇒h/ tanß+CD= h/tan∝`
`⇒ CD= h/tan∝-h/tanß`
`⇒ CD=h [1/tan∝-1/tanß]`
`⇒CD=h [cot ∝-cot ß]`
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