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A vertical pole stands at a point Q on a horizontal ground. A and B are points on the, ground, d meters apart. The pole subtends angles α and β at A and B respectively. AB subtends an angle γ at Q. Find the height of the pole.

A vertical pole stands at a point Q on a horizontal ground. A and B are points on the, ground, d meters apart. The pole subtends angles α and β at A and B respectively. AB subtends an angle γ  at Q. Find the height of the pole. 

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
6 years ago
Hello Student,
Please find the answer to your question
Let ht. of pole PQ be h.
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In ∆ APQ, tan α = h/AQ
⇒ AQ = h/tan α . . . . . . . . . . . . . . . . . . . . . . . . (1)
In ∆ BPQ, tan β = h/BQ ⇒ BQ = 4/tan β . . . . . . . . . . . . . . . . . . . . . . (2)
In ∆ ABQ, cos γ = AQ2 + BQ2 – AB2/2 AQ BQ
∴ cos γ = h2 cot2 α + h2 cot2 β –d2/2 h2 cot α cot β
∴ - 2h2 cot α cot β cos γ + h2 cot2 α + h2 cot2 β = d2
⇒ h = d/√cot2 α + cot2 β – 2 cot α cot β cos γ

Thanks
Aditi Chauhan
askIITians Faculty

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