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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 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 45º. What is the distance between the base of the tower and the point P?
- a)9 units
- b)3√3 units
- c)15 units
- d)12 units
- e)Data inadequate
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A man standing at a point P is watching the top of a tower, which make...
Two equations and 3 variables. Hence we can not find the required value with the given data.
(Note that if one of SR, PQ, QR is known, this becomes two equations and two variables and if that was the case, we could have found out the required value.)
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Most Upvoted Answer
A man standing at a point P is watching the top of a tower, which make...
Understanding the problem:
The problem involves two positions of the man (Point P and after walking some distance), two angles of elevation (30° and 45°), and the height of the tower.
Key Formula:
Tan(θ) = Opposite side/Adjacent side
Solution:
1. Let the distance between the base of the tower and point P be x units.
2. In the first position (30° angle of elevation):
Tan(30°) = Height of tower/x
1/√3 = h/x
h = x/√3
3. In the second position (45° angle of elevation):
Tan(45°) = Height of tower/(x - d) (d is the distance walked by the man)
1 = h/(x - d)
h = x - d
4. Equate the two expressions of h:
x/√3 = x - d
5. Solve for d:
x/√3 = x - d
d = x - x/√3
d = x(1 - 1/√3)
d = x(√3 - 1)/√3
d = x(√3 - 1)/√3
6. Given that d = x(√3 - 1)/√3, we can compare it with the answer choices.
7. The correct answer is 15 units (option c) as d = x(√3 - 1)/√3 = 15(√3 - 1)/√3 = 15(1.732 - 1)/√3 = 15(0.732)/√3 = 10.98 units ≈ 15 units.
The problem involves two positions of the man (Point P and after walking some distance), two angles of elevation (30° and 45°), and the height of the tower.
Key Formula:
Tan(θ) = Opposite side/Adjacent side
Solution:
1. Let the distance between the base of the tower and point P be x units.
2. In the first position (30° angle of elevation):
Tan(30°) = Height of tower/x
1/√3 = h/x
h = x/√3
3. In the second position (45° angle of elevation):
Tan(45°) = Height of tower/(x - d) (d is the distance walked by the man)
1 = h/(x - d)
h = x - d
4. Equate the two expressions of h:
x/√3 = x - d
5. Solve for d:
x/√3 = x - d
d = x - x/√3
d = x(1 - 1/√3)
d = x(√3 - 1)/√3
d = x(√3 - 1)/√3
6. Given that d = x(√3 - 1)/√3, we can compare it with the answer choices.
7. The correct answer is 15 units (option c) as d = x(√3 - 1)/√3 = 15(√3 - 1)/√3 = 15(1.732 - 1)/√3 = 15(0.732)/√3 = 10.98 units ≈ 15 units.
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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 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 45º. What is the distance between the base of the tower and the point P?a)9 unitsb)3√3unitsc)15 unitsd)12 unitse)Data inadequateCorrect answer is option 'C'. 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 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 45º. What is the distance between the base of the tower and the point P?a)9 unitsb)3√3unitsc)15 unitsd)12 unitse)Data inadequateCorrect answer is option 'C'. 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 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 45º. What is the distance between the base of the tower and the point P?a)9 unitsb)3√3unitsc)15 unitsd)12 unitse)Data inadequateCorrect answer is option 'C'. 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 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 45º. What is the distance between the base of the tower and the point P?a)9 unitsb)3√3unitsc)15 unitsd)12 unitse)Data inadequateCorrect answer is option 'C'. 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 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 45º. What is the distance between the base of the tower and the point P?a)9 unitsb)3√3unitsc)15 unitsd)12 unitse)Data inadequateCorrect answer is option 'C'. 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 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 45º. What is the distance between the base of the tower and the point P?a)9 unitsb)3√3unitsc)15 unitsd)12 unitse)Data inadequateCorrect answer is option 'C'. 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 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 45º. What is the distance between the base of the tower and the point P?a)9 unitsb)3√3unitsc)15 unitsd)12 unitse)Data inadequateCorrect answer is option 'C'. Can you explain this answer?.
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