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SSC CGL 2025 PYQ — Question 72

SSC CGL - 26 Sep 2025 - Shift 2 • Quantitative Aptitude • Q72

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The angles of elevation of the top of a cliff from two points on the ground, 200 m apart, and on opposite sides of the cliff, are 30° and 45°. What is the height of the cliff?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 100(3\sqrt{3} - 1) m.

Two points A and B are on opposite sides of the cliff (foot at point C).

Let the height of the cliff = h meters

From A: tan⁡30°=hAC\tan 30° = \frac{h}{AC}

⇒ 13=hAC\frac{1}{\sqrt{3}} = \frac{h}{AC}

⇒ AC=h3AC = h\sqrt{3}

From B: tan 45° = h/BC

⇒ 1 = h/BC

⇒ BC = h

AC + BC = 200

⇒ h√3 + h = 200

⇒ h(√3 + 1) = 200

⇒ h=2003+1=2003+1=200(3−1)(3+1)(3−1)=100(3−1)h = \frac{200}{\sqrt{3} + 1}= \frac{200}{\sqrt{3} + 1} = \frac{200(\sqrt{3} - 1)}{(\sqrt{3} + 1)(\sqrt{3} - 1)}= 100(\sqrt{3} - 1) m