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Home » A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h meter. At a point on the plane, the angle of elevation of the bottom of the flagstaff is α and at the top of the flagstaff is β. Prove that the height of the tower is h tan α/ (tan β – tan α).
A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h meter. At a point on the plane, the angle of elevation of the bottom of the flagstaff is α and at the top of the flagstaff is β. Prove that the height of the tower is h tan α/ (tan β – tan α).
Class 10 | Exercise 22C | Heights and Distances | ICSE | Selina
A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h meter. At a point on the plane, the angle of elevation of the bottom of the flagstaff is α and at the top of the flagstaff is β. Prove that the height of the tower is h tan α/ (tan β – tan α).

Selina Solutions Concise Class 10 Maths Chapter 22 ex. 22(C) - 8

SOLUTION:

Let AB be the tower of height x metre, surmounted by a vertical flagstaff AD. Let C be a point on the plane such that ∠ACB = α, ∠ACB = β and AD = h.

In ∆ABC,

    \[\begin{array}{*{35}{l}} AB/BC\text{ }=\text{ }tan\text{ }\alpha \\ BC\text{ }=\text{ }x/\text{ }tan\text{ }\alpha \text{ }\ldots \ldots .\text{ }\left( i \right) \\ \end{array}\]

In ∆DBC,

    \[\begin{array}{*{35}{l}} BD/BC\text{ }=\text{ }tan\text{ }\beta \\ BD\text{ }=\text{ }\left( x/tan\text{ }\alpha \right)\text{ }x\text{ }tan\text{ }\beta \text{ }\ldots \ldots \text{ }\left[ From\text{ }\left( i \right) \right] \\ \left( h\text{ }+\text{ }x \right)\text{ }tan\text{ }\alpha \text{ }=\text{ }x\text{ }tan\text{ }\beta \\ x\text{ }tan\text{ }\beta \text{ }-\text{ }x\text{ }tan\text{ }\alpha \text{ }=\text{ }h\text{ }tan\text{ }\alpha \\ \end{array}\]

Therefore, height of the tower is h tan α/ (tan β – tan α)

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