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Question
On the level ground, the angle of elevation of a tower is 30°. On moving 20 m nearer, the angle of elevation is 60°. The height of the tower is ______.
Options
10 m
`10sqrt(3)` m
15 m
20 m
MCQ
Fill in the Blanks
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Solution
On the level ground, the angle of elevation of a tower is 30°. On moving 20 m nearer, the angle of elevation is 60°. The height of the tower is `underlinebb(10sqrt(3) m)`.
Explanation:
`x/h = cot 60^circ = 1/sqrt(3)`
⇒ `x = h/sqrt(3)` ...(i)
`(x + 20)/h = cot 30^circ = sqrt(3)`
⇒ `x = (hsqrt(3) - 20)` ...(ii)
∴ `h/sqrt(3) = (hsqrt(3) - 20)`
⇒ `h = 3h - 20sqrt(3)`
⇒ `2h = 20sqrt(3)`
⇒ `h = 10sqrt(3)`
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