CDS 2026 (I) Elementary Mathematics, question 45

Topic: Heights and distances

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Q45

Two persons are on diametrically opposite sides of a tower. They measure the angles of elevation of the top of the tower as 30∘30^{\circ} and 60∘60^{\circ} respectively. If the height of the tower is 100100 m, what is the approximate distance between the two persons ?

  1. (a) 220 m
  2. (b) 225 m
  3. (c) 230 mCorrect answer
  4. (d) 235 m

Solution.

Answer: (c) 230 m

  1. The horizontal distances from the tower are 100cot⁡30∘=1003100\cot 30^{\circ} = 100\sqrt{3} and 100cot⁡60∘=100/3100\cot 60^{\circ} = 100/\sqrt{3}.
  2. Because the persons are on opposite sides, add the distances.
  3. Total =400/3= 400/\sqrt{3} ≈ 230.94 m.
  4. Among the listed choices, 230 m is closest.