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Ex 9.1, 15 - A straight highway leads to foot of a tower - Questions easy to difficult

  1. Chapter 9 Class 10 Some Applications of Trigonometry
  2. Serial order wise
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Ex 9.1 , 15 A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point. Let the man & tower height be AD Given that man sees car first at an angle of depression of 30° So, ∠ PAB = 30° After 6 seconds, the man sees car at an angle of depression of 60° So, ∠ PAC = 60° Now, tower is vertical, So, ∠ ADB = 90° Also, From (1) & (2) √3 CD = 𝐵𝐷/√3 √3 (√3 CD) = BD 3CD = BD 3CD = BC + CD 3CD – CD = BC 2CD = BC CD = 𝐵𝐶/2 Given that Time taken to cover BC = 6 seconds Time taken to cover 𝐵𝐶/2 = 6/2 seconds = 3 seconds ∴ Time taken to cover CD = 3 seconds

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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