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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 then the width of the river is :
  • a)
    3 (√3 –1)m
  • b)
    3 (√3 +1)m
  • c)
    (3 + √3)m
  • d)
    (3 – √3 )m.
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
From a point on a bridge across a river, the angles of depression of t...
° and 45°. If the bridge is 80 meters long, how wide is the river?

Let's label the diagram:

We want to find the width of the river, which is represented by the distance between points A and B.

To solve this problem, we need to use trigonometry. Specifically, we can use the tangent function:

tan(angle) = opposite/adjacent

We can use this formula for both angles of depression:

tan(30°) = AB/80

tan(45°) = AC/80

Simplifying these equations, we get:

AB = 80 tan(30°) ≈ 46.4 meters

AC = 80 tan(45°) ≈ 80 meters

Now we can use the Pythagorean theorem to find the length of BC:

BC^2 = AC^2 - AB^2

BC^2 = (80)^2 - (46.4)^2

BC ≈ 64.1 meters

Therefore, the width of the river (AB) is approximately 46.4 meters, and the length of the bridge (BC) is approximately 64.1 meters.
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From a point on a bridge across a river, the angles of depression of t...
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From a point on a bridge across a river, the angles of depression of the banks on opposite sidesof the river are 30° and 45° respectively. If the bridge is at a height of 3 m from the banks thenthe width of the river is :a)3 (√3–1)mb)3 (√3+1)mc)(3 + √3)md)(3 – √3)m.Correct answer is option 'B'. Can you explain this answer?
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From a point on a bridge across a river, the angles of depression of the banks on opposite sidesof the river are 30° and 45° respectively. If the bridge is at a height of 3 m from the banks thenthe width of the river is :a)3 (√3–1)mb)3 (√3+1)mc)(3 + √3)md)(3 – √3)m.Correct answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about From a point on a bridge across a river, the angles of depression of the banks on opposite sidesof the river are 30° and 45° respectively. If the bridge is at a height of 3 m from the banks thenthe width of the river is :a)3 (√3–1)mb)3 (√3+1)mc)(3 + √3)md)(3 – √3)m.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From a point on a bridge across a river, the angles of depression of the banks on opposite sidesof the river are 30° and 45° respectively. If the bridge is at a height of 3 m from the banks thenthe width of the river is :a)3 (√3–1)mb)3 (√3+1)mc)(3 + √3)md)(3 – √3)m.Correct answer is option 'B'. Can you explain this answer?.
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