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GATE 2024 EE – Question 10

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

A surveyor has to measure the horizontal distance from her position to a distant reference point C. Using her position as the center, a 200 m horizontal line segment is drawn with the two endpoints A and B. Points A, B, and C are not collinear. Each of the angles ∠CAB and ∠CBA are measured as 87.8°. The distance (in m) of the reference point C from her position is nearest to

  1. 2603
  2. 2606
  3. 2306
  4. 2063

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Show answer and explanation

Correct answer: (A) 2603

Explanation

Triangle $ABC$ is isosceles ($\angle A=\angle B$), so $C$ lies on the perpendicular bisector of $AB$ through her position (the midpoint). Its distance from the midpoint is $100\tan87.8^\circ=100\times26.03=2603$ m.