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A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of elevation becomes 60°. What is the distance between the base of the tower and the point P?
- a)4(3)^0.5 units
- b)8 units
- c)12 units
- d)6 units
- e)Data inadequate
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
A man standing at a point P is watching the top of a tower, which make...
Let MN be the tower and man be standing at P (30° = angle MPN) and Q (60° = angle MQN). We are only given two angles and no sides of the triangles. Therefore, the data is inadequate.
Most Upvoted Answer
A man standing at a point P is watching the top of a tower, which make...
Given:
- Angle of elevation from point P to the top of the tower is 30°.
- When the man walks closer to the tower, the angle of elevation becomes 60°.
Approach:
- Let the distance between the base of the tower and point P be x units.
- Let the height of the tower be h units.
Calculations:
- In triangle PQT (where T is the top of the tower):
- tan 30° = h/x
- h = x * tan 30° = x * (√3)/3
- In triangle PRS (where R is the new position of the man):
- tan 60° = h/(x - d), where d is the distance the man walked closer to the tower.
- h = (x - d) * tan 60° = (x - d) * √3
- Equating the two expressions for h:
- x * (√3)/3 = (x - d) * √3
- x/3 = x - d
- d = 2x/3
Conclusion:
- The distance between the base of the tower and the point P (x) is related to the distance the man walked closer to the tower (d) by d = 2x/3.
- The relationship between x and d does not provide a unique solution for x, hence the data provided is inadequate to determine the distance between the base of the tower and point P.
- Angle of elevation from point P to the top of the tower is 30°.
- When the man walks closer to the tower, the angle of elevation becomes 60°.
Approach:
- Let the distance between the base of the tower and point P be x units.
- Let the height of the tower be h units.
Calculations:
- In triangle PQT (where T is the top of the tower):
- tan 30° = h/x
- h = x * tan 30° = x * (√3)/3
- In triangle PRS (where R is the new position of the man):
- tan 60° = h/(x - d), where d is the distance the man walked closer to the tower.
- h = (x - d) * tan 60° = (x - d) * √3
- Equating the two expressions for h:
- x * (√3)/3 = (x - d) * √3
- x/3 = x - d
- d = 2x/3
Conclusion:
- The distance between the base of the tower and the point P (x) is related to the distance the man walked closer to the tower (d) by d = 2x/3.
- The relationship between x and d does not provide a unique solution for x, hence the data provided is inadequate to determine the distance between the base of the tower and point P.
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A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of elevation becomes 60°. What is the distance between the base of the tower and the point P?a)4(3)^0.5 unitsb)8 unitsc)12 unitsd)6 unitse)Data inadequateCorrect answer is option 'E'. Can you explain this answer?
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A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of elevation becomes 60°. What is the distance between the base of the tower and the point P?a)4(3)^0.5 unitsb)8 unitsc)12 unitsd)6 unitse)Data inadequateCorrect answer is option 'E'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of elevation becomes 60°. What is the distance between the base of the tower and the point P?a)4(3)^0.5 unitsb)8 unitsc)12 unitsd)6 unitse)Data inadequateCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of elevation becomes 60°. What is the distance between the base of the tower and the point P?a)4(3)^0.5 unitsb)8 unitsc)12 unitsd)6 unitse)Data inadequateCorrect answer is option 'E'. Can you explain this answer?.
A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of elevation becomes 60°. What is the distance between the base of the tower and the point P?a)4(3)^0.5 unitsb)8 unitsc)12 unitsd)6 unitse)Data inadequateCorrect answer is option 'E'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of elevation becomes 60°. What is the distance between the base of the tower and the point P?a)4(3)^0.5 unitsb)8 unitsc)12 unitsd)6 unitse)Data inadequateCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of elevation becomes 60°. What is the distance between the base of the tower and the point P?a)4(3)^0.5 unitsb)8 unitsc)12 unitsd)6 unitse)Data inadequateCorrect answer is option 'E'. Can you explain this answer?.
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