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Example 7 - From a point on a bridge across a river - Questions easy to difficult

  1. Chapter 9 Class 10 Some Applications of Trigonometry
  2. Serial order wise
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Example 7 From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45°, respectively. If the bridge is at a height of 3 m from the banks, find the width of the river. Let the width of the river = AB And the bridge is at a height of 3m from the banks, So, DP = 3 metre Angle of depression of the banks on opposite sides of the river are 30° and 45° respectively. So, ∠ QPA = 30° and ∠ RPB = 45° We need to find width of river i.e. AB Since PD is the height, it is perpendicular to AB ∠ PDA = ∠ PDB = 90° Lines PQ & AB are parallel, And AP is the transversal ∴ ∠ PAD = ∠ QPA ⇒ ∠ PAD = 30° Similarly, Lines PR & AB are parallel, And BP is the transversal ∴ ∠ PBD = ∠ RPB ⇒ ∠ PBD = 45° Now, AB = AD + BD = 3√3 + 3 = 3(√3 + 1) ∴ Width of the river = AB = 3(√3 + 1) metre

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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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