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A man wishes to find the height of the building which stands on a horizontal plane. At a point on the plane, he finds the angle of elevation of the top of the building to be 60° and moving 10 m along the same line away from the building he finds the angle of elevation to be 30°. What is the height of the building?

A man wishes to find the height of the building which stands on a horizontal plane. At a point on the plane, he finds the angle of elevation of the top of the building to be 60° and moving 10 m along the same line away from the building he finds the angle of elevation to be 30°. What is the height of the building? Correct Answer 5√3

Given:

The angle of elevation of 60° and 30° respectively.

Concept:

tanθ = (Perpendicular)/(Base)

Calculation:

⇒ Let AB be the height of the building.

⇒ From ΔABC, tan60° = (AB)/(BC)

⇒ BC = h/√3      ....(1)

⇒ From ΔABD, tan30° = (AB)/(BD)

⇒ (AB)/(BC + CD) = 1/√3

⇒ √3(AB) = BC + 10

⇒ BC = √3h - 10     ....(2)

⇒ From (1) and (2)

⇒ h/√3 = √3h - 10

⇒ h = 3h - 10√3

⇒ 2h = 10√3

⇒ h = 5√3

∴ The required result will be 5√3.

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