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Ex 9.1, 11 - A TV tower stands vertically on a bank of canal - Questions easy to difficult

  1. Chapter 9 Class 10 Some Applications of Trigonometry
  2. Serial order wise
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Ex 9.1 , 11 A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30° (see figure). Find the height of the tower and the width of the canal. Let tower be AB So, height of tower = AB Given that,from a point on the other bank directly opposite the Tower,the angle of elevation of the tower is 60°. Hence, ∠ACB = 30° Also, Angle of elevation from point D to top of the tower = 30° So, ∠ ADB = 30° Also, DC = 20 m We need to find height of tower AB & width of canal BC Since tower is vertical to ground So, ∠ ABD = 90° From (1) & (2) √3BC = 𝐵𝐷/√3 √3×√3BC = BD 3BC = BD 3BC = BC + CD 3BC = BC + 20 3BC – BC = 20 2BC = 20 BC = 20/2 BC = 10 m Hence, the width of the canal is 10 m From (1) AB = √3BC AB = √3 × 10 AB = 10√3 m Hence, height of tower = 10√3 m

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