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The angle of elevation of the top of a tower, vertically erected in the middle of a paddy field, from two points on a horizontal line through the foot of the tower are given to be α and β (α > β). The height of the tower is h unit. A possible distance (in the same unit) between the points is
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h(cot β - cot α) metre cos(α + β) - h (cot α - cot β)
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h(tan β - tan α) metre tan α tan β) - h (cot α + cot β)
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Correct Option: D
Let AB = height of tower = h metre
∠ACB = α ; ∠ADB = β
In ∆ABC,
| tan α = | BC |
| ⇒ tan α = | ⇒ BC = | BC | tan α |
= h cotα
In ∆ABD,
| ⇒ tan β = | ⇒ tan β = | BD | BD |
| ⇒ BD = | = h cot β | tan β |
∴ BC = BC + BD
= h cotα + h cotβ
= h (cotα + cotβ)
