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 If the angles of depression from the top of a tower of height 40 m to the top and bottom of a tree are 45° and 60° respectively, then the height of the tree is
  • a)
  • b)
  • c)
  • d)
    None of the above
Correct answer is option 'B'. Can you explain this answer?
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If the angles of depression from the top of a tower of height 40 m to ...
A tower of height 40 m is given, and the angles of depression from the top of the tower to:
  • The top of the tree = 45°
  • The bottom of the tree = 60°
We need to find the height of the tree (h).
Step 1: Use trigonometry for the angles of depression
Let:
  • The distance between the base of the tower and the base of the tree = d
  • The height of the tree = h
From the 45° angle (to the top of the tree):
The formula is:
tan(45°) = (Height of the tower - Height of the tree) / Distance (d)
Since tan(45°) = 1:
1 = (40 - h) / d
d = 40 - h (1)
From the 60° angle (to the bottom of the tree):
The formula is:
tan(60°) = Height of the tower / Distance (d)
Since tan(60°) = √3:
√3 = 40 / d
d = 40 / √3 (2)
Step 2: Solve the equations
Equate d from equations (1) and (2):
40 - h = 40 / √3
Rearrange to solve for h:
h = 40 - (40 / √3)
Rationalize the denominator:
h = 40 - (40√3 / 3)
h = (120 / 3) - (40√3 / 3)
h = (40 (3 - √3)) / 3
The height of the tree is:
b) (40 / 3) (3 - √3)
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If the angles of depression from the top of a tower of height 40 m to the top and bottom of a tree are 45° and 60° respectively, then the height of the tree isa)b)c)d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If the angles of depression from the top of a tower of height 40 m to the top and bottom of a tree are 45° and 60° respectively, then the height of the tree isa)b)c)d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the angles of depression from the top of a tower of height 40 m to the top and bottom of a tree are 45° and 60° respectively, then the height of the tree isa)b)c)d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
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