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प्रश्न
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 30°. Determine the height of the tower.
उत्तर
Given, height of building = 7 m
Let AC = h m and BD = x m
In ΔBDE,
tan 30° = `(ED)/(BD)`
`\implies = 1/sqrt(3) = 7/x`
`\implies` x = `7sqrt(3)` m
In ΔACE,
tan 60° = `(AC)/(CE)`
`\implies sqrt(3) = h/x` ...[∵ CE = BD]
`\implies` h = `xsqrt(3)`
= `7sqrt(3) xx sqrt(3)`
= 7 × 3
= 21 m
∴ Height of the tower = AB = AC + CB
= 21 + 7
= 28 m.
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