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All questions of Height & Distance for CDS Exam
From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 100 m high, the distance of point P from the foot of the tower is:- a)149 m
- b)156 m
- c)173 m
- d)200 m
Correct answer is option 'C'. Can you explain this answer?
From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 100 m high, the distance of point P from the foot of the tower is:
a)
149 m
b)
156 m
c)
173 m
d)
200 m
|
Anjana Joshi answered |
From a point P on a level ground, the angle of elevation of the top tower is 30 degrees.
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 60º. What is the distance between the base of the tower and the point P?- a)4√3 units
- b)8 units
- c)12 units
- d)Data inadequate
- e)None of these
Correct answer is option 'D'. 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 60º. What is the distance between the base of the tower and the point P?
a)
4√3 units
b)
8 units
c)
12 units
d)
Data inadequate
e)
None of these
|
Kalyan Mukherjee answered |
Practice Quiz or MCQ (Multiple Choice Questions) with solution are available for Practice, which would help you prepare for "Height and Distance" under Logical Reasoning and Data Interpretative. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.Q.Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:- a)173 m
- b)200 m
- c)273 m
- d)300 m
Correct answer is option 'C'. Can you explain this answer?
Practice Quiz or MCQ (Multiple Choice Questions) with solution are available for Practice, which would help you prepare for "Height and Distance" under Logical Reasoning and Data Interpretative. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.
Q.
Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:
a)
173 m
b)
200 m
c)
273 m
d)
300 m
|
|
Shruti Reddy answered |
Understanding the Problem
We have two ships on either side of a lighthouse that is 100 m high. The angles of elevation to the top of the lighthouse from the ships are 30° and 45°. We need to find the distance between the two ships.
Step 1: Calculate the Distances from Each Ship to the Lighthouse
- Ship A (Angle of Elevation = 30°):
- Using the tangent function:
- tan(30°) = Height / Distance
- tan(30°) = 100 / Distance_A
- Distance_A = 100 / tan(30°) = 100 / (1/√3) = 100√3 m ≈ 173.21 m
- Ship B (Angle of Elevation = 45°):
- Again using the tangent function:
- tan(45°) = Height / Distance
- tan(45°) = 100 / Distance_B
- Distance_B = 100 / tan(45°) = 100 / 1 = 100 m
Step 2: Calculate the Total Distance Between the Two Ships
- Total Distance between Ships:
- The total distance between the two ships is the sum of the distances from each ship to the lighthouse.
- Distance = Distance_A + Distance_B
- Distance = 173.21 m + 100 m = 273.21 m
Conclusion
Thus, the distance between the two ships is approximately 273 m.
The correct answer is option 'C'.
We have two ships on either side of a lighthouse that is 100 m high. The angles of elevation to the top of the lighthouse from the ships are 30° and 45°. We need to find the distance between the two ships.
Step 1: Calculate the Distances from Each Ship to the Lighthouse
- Ship A (Angle of Elevation = 30°):
- Using the tangent function:
- tan(30°) = Height / Distance
- tan(30°) = 100 / Distance_A
- Distance_A = 100 / tan(30°) = 100 / (1/√3) = 100√3 m ≈ 173.21 m
- Ship B (Angle of Elevation = 45°):
- Again using the tangent function:
- tan(45°) = Height / Distance
- tan(45°) = 100 / Distance_B
- Distance_B = 100 / tan(45°) = 100 / 1 = 100 m
Step 2: Calculate the Total Distance Between the Two Ships
- Total Distance between Ships:
- The total distance between the two ships is the sum of the distances from each ship to the lighthouse.
- Distance = Distance_A + Distance_B
- Distance = 173.21 m + 100 m = 273.21 m
Conclusion
Thus, the distance between the two ships is approximately 273 m.
The correct answer is option 'C'.
Chapter doubts & questions for Height & Distance - Elementary Mathematics for CDS 2025 is part of CDS exam preparation. The chapters have been prepared according to the CDS exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for CDS 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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Elementary Mathematics for CDS
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