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Ankit and Priya stand on opposite sides of a clock tower 45 m tall, in a straight line with its foot.
Ankit sees the top at an angle of elevation of 60°, and Priya sees it at an angle of elevation of 30°.
A student writes: 'Ankit's distance from the foot = 45 m and Priya's distance from the foot = m.'
What is the error?

Class 10Heights and DistancesTrigonometry
  • AThere is no error; both distances are correct as written.
  • BThe two distances have been interchanged: the larger angle of 60° must give the SMALLER distance, so Ankit is m away and Priya is 45 m away.
  • CBoth distances should be doubled, because the tower is being seen from two opposite sides.
  • DThe distances should have been found using sin instead of tan, giving 90 m for each observer.

Step-by-Step Solution

For Ankit, tan m (about 25.98 m). For Priya, tan m (about 77.94 m). The student swapped them: a steeper line of sight always means the observer is nearer to the foot.
Answer: B) The two distances have been interchanged: the larger angle of 60° must give the SMALLER distance, so Ankit is m away and Priya is 45 m away.

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