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A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angle of elevation of the bottom of the flag staff is a and that of the top of the flag staff is β. Then the height of the tower is
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- h tanα
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h tan α tan β - tan α -
h tan α tan α - tan β - None of these
Correct Option: B
Let height of tower = BC = y metre
AB = height of flag-staff = h metre
∠BDC = a; ∠ADC = b
Let, CD = x metre
In ∆BCD,
| tan α = | CD |
| ⇒ tan α = | ..... (i) | x |
In ∆ACD,
| tan β = | CD |
| ⇒ tan β = | x |
| ⇒ x = | ..... (ii) | tanβ |
| ∴ | = | tanα | tanβ |
⇒ y tan β = h tanα + y tanα
⇒ y tanβ – y tanα = h tanα
⇒ y (tanβ – tanα) = h tanα
| ⇒ y = | tanβ - tanα |
