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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 α and β (β > α). Find the distance between the two objects .

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Solution


Let the two objects be at points C and D.
The angle of depression for the point C is β and for the point D is α.
In ∆ABC,
tanβ=hBCBC=htanβ
In ∆ABD,
tanα=hBDtanα=hBC+CDtanα=hhtanβ+CDhtanβ+CD=htanα
CD=htanα-htanβCD=h1tanα-1tanβCD=hcotα-cotβ

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