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SSC CGL 2023 PYQ — Question 2

SSC CGL Tier II - 26 October 2023 • Quantitative Aptitude • Q2

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From the top of a tower, the angle of depression of the top of a 10 m high building is 60o. If the distance between the tower and the building is 50350\sqrt{3} m, find the height of the tower.

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 160 m.

As seen in the figure

∠ADC = 60° (alternate interior angles)

Let the height of AC = x

Tanθ = PerpendicularBase\frac{Perpendicular}{Base}

Now, Tan ADC = x50√3\frac{x}{50√3}

⇒ Tan 60 = x50√3\frac{x}{50√3}

⇒ √3 = x50√3\frac{x}{50√3}

⇒ x = 50 × 3 = 150

Hence the height of the tower = 150 + 10 = 160 m.