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The difference in the lengths of the shadows of a pole cast by the sun (at different times of a day) when the angles of elevation of the top of the pole measured from two points on the ground on the same side of the pole were 45° and 30° was given as \(10(\sqrt 3 - 1) m.\) How tall was the pole?

The difference in the lengths of the shadows of a pole cast by the sun (at different times of a day) when the angles of elevation of the top of the pole measured from two points on the ground on the same side of the pole were 45° and 30° was given as \(10(\sqrt 3 - 1) m.\) How tall was the pole? Correct Answer 10 m

Concept:

  • tan θ = perpendicular/base
  • tan 30° = 1/√3 

  • tan 45° = 1

Calculation:

⇒ h - h√3 = 10 - 10√3 

⇒ h(1 - √3) = 10(1 - √3)

⇒ h = 10 m

Hence, the height of the pole is 10 m.

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