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SSC CPO 2025 PYQ — Question 105

SSC CPO - 9 Dec 2025 - Shift 2 • Quantitative Aptitude • Q105

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From the summit of a 90-meter-high building, the angles of depression to the top and bottom of a tower are measured at 30° and 60°, respectively. What is the height of the tower in meters?

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Correct answer: B

Explanation

Let the height of the tower be h and the horizontal distance be x.
tan⁡60∘=90x3=90xx=903=303tan⁡30∘=90−hx13=90−h30390−h=30h=60\tan 60^\circ = \frac{90}{x} \\ \sqrt{3} = \frac{90}{x} \\ x = \frac{90}{\sqrt{3}} = 30\sqrt{3} \\ \tan 30^\circ = \frac{90 - h}{x} \\ \frac{1}{\sqrt{3}} = \frac{90 - h}{30\sqrt{3}} \\ 90 - h = 30 \\ h = 60