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A man standing at a point X on the bank XY of a river that cannot be crossed, observes a tower to be N α° E on the opposite parallel bank. He then walks 200 m along the bank to the point Y towards East, and finds the tower to be N β° W. From the observation what is the breadth of the river will be
(Given that the tanα° = 2 and tanβ° = 0.5)
  • a)
    60 m
  • b)
    70 m
  • c)
    80 m
  • d)
    90 m
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A man standing at a point X on the bank XY of a river that cannot be c...

In triangle TXY
∠X = 90° - α and ∠Y = 90° - β
Let the height be TM
⇒ TM/MX = tan(90 - α)
⇒ TM/MX = cotα = 1/tanα = 1/2
∴ MX = 2TM
Similarly
TM/MY = tan(90 - β)
⇒ TM/MY = cot(90 - β) = 1/tan β = 1/0.5
∴ MY = 0.5TM
XY = MX + MY
⇒ 200 = 2TM + 0.5TM
⇒ 200 = 2.5TM
∴ TM = 80 m
∴ Distance between the banks = 80 m
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A man standing at a point X on the bank XY of a river that cannot be c...
Orthwest of him. He walks 200 meters to a point Z on the bank XZ, in the line of the tower and finds the angle of elevation of the top of the tower to be 30 degrees. If the width of the river is 100 meters, find the height of the tower.
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A man standing at a point X on the bank XY of a river that cannot be crossed, observes a tower to be N α° E on the opposite parallel bank. He then walks 200 m along the bank to the point Y towards East, and finds the tower to be N β° W. From the observation what is the breadth of the river will be(Given that the tanα° = 2 and tanβ° = 0.5)a)60 mb)70 mc)80 md)90 mCorrect answer is option 'C'. Can you explain this answer?
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A man standing at a point X on the bank XY of a river that cannot be crossed, observes a tower to be N α° E on the opposite parallel bank. He then walks 200 m along the bank to the point Y towards East, and finds the tower to be N β° W. From the observation what is the breadth of the river will be(Given that the tanα° = 2 and tanβ° = 0.5)a)60 mb)70 mc)80 md)90 mCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A man standing at a point X on the bank XY of a river that cannot be crossed, observes a tower to be N α° E on the opposite parallel bank. He then walks 200 m along the bank to the point Y towards East, and finds the tower to be N β° W. From the observation what is the breadth of the river will be(Given that the tanα° = 2 and tanβ° = 0.5)a)60 mb)70 mc)80 md)90 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man standing at a point X on the bank XY of a river that cannot be crossed, observes a tower to be N α° E on the opposite parallel bank. He then walks 200 m along the bank to the point Y towards East, and finds the tower to be N β° W. From the observation what is the breadth of the river will be(Given that the tanα° = 2 and tanβ° = 0.5)a)60 mb)70 mc)80 md)90 mCorrect answer is option 'C'. Can you explain this answer?.
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