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A person is standing in front of the Burj Khalifa building, the angle of elevation from a particular point on the ground to the top of the building is 30°. When he walks 30 meters towards the building he finds his angle of elevation to be 60°. Find the height of the Burj Khalifa building?

A person is standing in front of the Burj Khalifa building, the angle of elevation from a particular point on the ground to the top of the building is 30°. When he walks 30 meters towards the building he finds his angle of elevation to be 60°. Find the height of the Burj Khalifa building? Correct Answer 15√3 m

Given:

The angle of elevation when he is at 40 meters from the foot of the building at point B is ∠B = 30°

The angle of elevation after he walks 30 meters towards the building at point D, is ∠D = 60°

The distance walked towards the building = 30 m

Concept used:

Using the concept of a trigonometric ratio

Calculation:

Let us depict the given information on a diagram

In ΔACD,

tan60° = AC/CD

⇒ √3 = H/CD

⇒ CD = H/√3

In ΔABC,

tan30° = AC/BC

⇒ 1/√3 = H/(30 + CD)

⇒ √3H = 30 + H/√3

⇒ √3H - H/√3 = 30

⇒ (3H - H)/√3 = 30

⇒ 2H/√3 = 30

⇒ H = 15√3 m

∴ The height of the Burj Khalifa building is 15√3 m.

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