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From the top of a cliff 25m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower the height of the tower is?
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From the top of a cliff 25m high the angle of elevation of a tower is ...
Given data:
- Height of the cliff: 25m
Approach:
- We can use trigonometry to solve this problem by considering the right triangle formed by the cliff, the tower, and the horizontal distance between them.
- The angle of elevation from the top of the cliff to the top of the tower is equal to the angle of depression from the top of the tower to the foot of the tower.
- Let the height of the tower be h and the horizontal distance between the cliff and the tower be x.
Calculations:
- tan(angle of elevation) = h/x
- tan(angle of depression) = h/x
- tan(angle of elevation) = tan(angle of depression)
- h/25 = h/x
- x = 25
- Using Pythagoras theorem: x^2 + h^2 = (25+h)^2
- 25^2 + h^2 = (25+h)^2
- 625 + h^2 = 625 + 50h + h^2
- 50h = 625
- h = 12.5m
Conclusion:
- The height of the tower is 12.5 meters.
- Height of the cliff: 25m
Approach:
- We can use trigonometry to solve this problem by considering the right triangle formed by the cliff, the tower, and the horizontal distance between them.
- The angle of elevation from the top of the cliff to the top of the tower is equal to the angle of depression from the top of the tower to the foot of the tower.
- Let the height of the tower be h and the horizontal distance between the cliff and the tower be x.
Calculations:
- tan(angle of elevation) = h/x
- tan(angle of depression) = h/x
- tan(angle of elevation) = tan(angle of depression)
- h/25 = h/x
- x = 25
- Using Pythagoras theorem: x^2 + h^2 = (25+h)^2
- 25^2 + h^2 = (25+h)^2
- 625 + h^2 = 625 + 50h + h^2
- 50h = 625
- h = 12.5m
Conclusion:
- The height of the tower is 12.5 meters.
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From the top of a cliff 25m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower the height of the tower is?
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From the top of a cliff 25m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower the height of the tower is? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about From the top of a cliff 25m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower the height of the tower is? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From the top of a cliff 25m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower the height of the tower is?.
From the top of a cliff 25m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower the height of the tower is? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about From the top of a cliff 25m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower the height of the tower is? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From the top of a cliff 25m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower the height of the tower is?.
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