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JEE Main 2004
Exam
JEE Main
Year
2004
Subject
Mathematics
Chapter
Heights and Distances

JEE Main 2004 · Mathematics · Heights and Distances

A person standing on the bank of a river observes that the angle of...

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60∘60^{\circ} and when he retires 40 meter away from the tree the angle of elevation becomes 30∘30^{\circ}. The breadth of the river isA person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank

Options

  1. A20 m20 \mathrm{~m}
  2. B30 m30 \mathrm{~m}
  3. C40 m40 \mathrm{~m}
  4. D60 m60 \mathrm{~m}

Correct answer

A. 20 m20 \mathrm{~m}

Step-by-step solution

tan⁡30∘=h40+b\tan 30^{\circ}=\frac{h}{40+b} ⇒3h=40+b\Rightarrow \sqrt{3} h=40+b tan⁡60∘=h/b⇒h=3b\tan 60^{\circ}=h / b \Rightarrow h=\sqrt{3} b ⇒b=20m\Rightarrow b=20 m A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank
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