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Two towers of the same height stand on opposite sides of a road 100 m wide. At a point on the road between the towers, the elevations of the towers are 30° and 45°. Find the height of the towers and the position of the point from the farthest tower.
  • a)
    36.6 m and 63.4 m
  • b)
    63.3 m and 63.4 m
  • c)
    66.3 m and 63.4 m
  • d)
    36.6 m and 86.4 m
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Two towers of the same height stand on opposite sides of a road 100 m...
Let AB, CD are towers
E is the point between road BC.
Then in △DCE
CD = EC = X = AB
IN △ABE
BE= √3x then
Position of the farthest tower from point = 63.4 mtr.
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Most Upvoted Answer
Two towers of the same height stand on opposite sides of a road 100 m...
Let AB, CD are towers
E is the point between road BC.
Then in △DCE
CD = EC = X = AB
IN △ABE
BE= √3x then
Position of the farthest tower from point = 63.4 mtr.
Free Test
Community Answer
Two towers of the same height stand on opposite sides of a road 100 m...



Given Data:
- Elevation of the first tower = 30°
- Elevation of the second tower = 45°
- Distance between the towers = 100 m

Calculations:
- Let the height of the towers be 'h' meters
- Let the distance from the point on the road to the farthest tower be 'x' meters

Using trigonometry:
- In the first tower, tan(30°) = h/x
- In the second tower, tan(45°) = h/(100-x)

Solving the equations:
- tan(30°) = h/x
- tan(45°) = h/(100-x)
- h = x * tan(30°)
- h = (100-x) * tan(45°)
- x * tan(30°) = (100-x) * tan(45°)
- x * 0.5774 = (100-x) * 1
- 0.5774x = 100 - x
- 1.5774x = 100
- x = 63.4 m

Substitute x back into the equations to find h:
- h = 63.4 * tan(30°)
- h = 36.6 m
Therefore, the height of the towers is 36.6 m and the position of the point from the farthest tower is 63.4 m.

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Two towers of the same height stand on opposite sides of a road 100 m wide. At a point on the road between the towers, the elevations of the towers are 30° and 45°. Find the height of the towers and the position of the point from the farthest tower.a)36.6 m and 63.4 mb)63.3 m and 63.4 mc)66.3 m and 63.4 md)36.6 m and 86.4 mCorrect answer is option 'A'. Can you explain this answer?
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Two towers of the same height stand on opposite sides of a road 100 m wide. At a point on the road between the towers, the elevations of the towers are 30° and 45°. Find the height of the towers and the position of the point from the farthest tower.a)36.6 m and 63.4 mb)63.3 m and 63.4 mc)66.3 m and 63.4 md)36.6 m and 86.4 mCorrect answer is option 'A'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Two towers of the same height stand on opposite sides of a road 100 m wide. At a point on the road between the towers, the elevations of the towers are 30° and 45°. Find the height of the towers and the position of the point from the farthest tower.a)36.6 m and 63.4 mb)63.3 m and 63.4 mc)66.3 m and 63.4 md)36.6 m and 86.4 mCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two towers of the same height stand on opposite sides of a road 100 m wide. At a point on the road between the towers, the elevations of the towers are 30° and 45°. Find the height of the towers and the position of the point from the farthest tower.a)36.6 m and 63.4 mb)63.3 m and 63.4 mc)66.3 m and 63.4 md)36.6 m and 86.4 mCorrect answer is option 'A'. Can you explain this answer?.
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