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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

Correct answer: 2603

Solution

With AB=200 and base angles 87.8 degrees, the apex C lies above the midpoint; its distance is 100*tan(87.8)=100*26.03=2603 m. The stored 2063 is wrong; the answer is 2603.

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