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From a point P, the angle of elevation of a tower is such that its tangent is 3/4. On walking 560 metres towards the tower the tangent of the angle of elevation of the tower becomes 4/3. What is the height (in metres) of the tower?

From a point P, the angle of elevation of a tower is such that its tangent is 3/4. On walking 560 metres towards the tower the tangent of the angle of elevation of the tower becomes 4/3. What is the height (in metres) of the tower? Correct Answer 960

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Let OP = x mtr and RO = h mtr

Given tan ∠RPO = ¾

⇒ h/x = 3/4

⇒ 4h = 3x       ---- (1)

Given tan∠RQO = 4/3

⇒ h/ (x – 560) = 4/3

⇒ 3h = 4x – 2240

From equation (1)

⇒ 3h = 16h/3 – 2240

⇒ 7h/3 = 2240

⇒ h = 960 mtr

∴ Height of the tower is 960 mtr

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