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An aeroplane when 750 m high passes vertically above another aeroplane at an instant when their angles of elevation at same observing point are 45° and 30&de; respectively. Approximately, how many meters higher is the one than the other?
- a)250(1- √3)
- b)750(3- √3)
- c)250(3- √3)
- d)275(1- √3)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
An aeroplane when 750 m high passes vertically above another aeroplane...
Let C and D be the position of the aeroplanes.
Given that CB = 900 m,∠CAB = 60°,∠DAB = 45°
From the right △ ABC,
Tan45 = CB/AB => CB = AB
From the right △ ADB,
Tan30 = DB/AB => DB = ABtan30 = CBx(1/√3) = 750/√3
CB = CD + DB
=> Required height CD = CB - DB = 750 - 750/√3 = 250(3 - √3)
Most Upvoted Answer
An aeroplane when 750 m high passes vertically above another aeroplane...
Understanding the Problem
We need to determine how much higher one aeroplane is compared to another when they are observed from a point on the ground.
Given Data
- Height of the first aeroplane (A) = 750 m
- Angle of elevation to A = 45°
- Angle of elevation to the second aeroplane (B) = 30°
Visualizing the Situation
1. Let the observer be at point O.
2. The height of aeroplane A (750 m) creates a right triangle where:
- Height (hA) = 750 m
- Angle (θA) = 45°
3. For aeroplane B, let its height be hB, creating another right triangle:
- Angle (θB) = 30°
Using Trigonometry
- For aeroplane A:
- tan(45°) = hA / d → d = hA (since tan(45°) = 1)
- Therefore, d = 750 m
- For aeroplane B:
- tan(30°) = hB / d
- Substituting d = 750 m → √3/3 = hB / 750
- hB = 750 * √3 / 3 = 250√3 m
Finding the Height Difference
- Now, to find how much higher aeroplane A is than B:
- Height difference = hA - hB
- Height difference = 750 - 250√3
Final Calculation
- Factor out 250:
- Height difference = 250(3 - √3)
Thus, the approximate height difference between the two aeroplanes is 250(3 - √3) meters, corresponding to option 'C'.
We need to determine how much higher one aeroplane is compared to another when they are observed from a point on the ground.
Given Data
- Height of the first aeroplane (A) = 750 m
- Angle of elevation to A = 45°
- Angle of elevation to the second aeroplane (B) = 30°
Visualizing the Situation
1. Let the observer be at point O.
2. The height of aeroplane A (750 m) creates a right triangle where:
- Height (hA) = 750 m
- Angle (θA) = 45°
3. For aeroplane B, let its height be hB, creating another right triangle:
- Angle (θB) = 30°
Using Trigonometry
- For aeroplane A:
- tan(45°) = hA / d → d = hA (since tan(45°) = 1)
- Therefore, d = 750 m
- For aeroplane B:
- tan(30°) = hB / d
- Substituting d = 750 m → √3/3 = hB / 750
- hB = 750 * √3 / 3 = 250√3 m
Finding the Height Difference
- Now, to find how much higher aeroplane A is than B:
- Height difference = hA - hB
- Height difference = 750 - 250√3
Final Calculation
- Factor out 250:
- Height difference = 250(3 - √3)
Thus, the approximate height difference between the two aeroplanes is 250(3 - √3) meters, corresponding to option 'C'.
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An aeroplane when 750 m high passes vertically above another aeroplane at an instant when their angles of elevation at same observing point are 45° and 30&de; respectively. Approximately, how many meters higher is the one than the other?a)250(1- √3)b)750(3- √3)c)250(3- √3)d)275(1- √3)Correct answer is option 'C'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about An aeroplane when 750 m high passes vertically above another aeroplane at an instant when their angles of elevation at same observing point are 45° and 30&de; respectively. Approximately, how many meters higher is the one than the other?a)250(1- √3)b)750(3- √3)c)250(3- √3)d)275(1- √3)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An aeroplane when 750 m high passes vertically above another aeroplane at an instant when their angles of elevation at same observing point are 45° and 30&de; respectively. Approximately, how many meters higher is the one than the other?a)250(1- √3)b)750(3- √3)c)250(3- √3)d)275(1- √3)Correct answer is option 'C'. Can you explain this answer?.
An aeroplane when 750 m high passes vertically above another aeroplane at an instant when their angles of elevation at same observing point are 45° and 30&de; respectively. Approximately, how many meters higher is the one than the other?a)250(1- √3)b)750(3- √3)c)250(3- √3)d)275(1- √3)Correct answer is option 'C'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about An aeroplane when 750 m high passes vertically above another aeroplane at an instant when their angles of elevation at same observing point are 45° and 30&de; respectively. Approximately, how many meters higher is the one than the other?a)250(1- √3)b)750(3- √3)c)250(3- √3)d)275(1- √3)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An aeroplane when 750 m high passes vertically above another aeroplane at an instant when their angles of elevation at same observing point are 45° and 30&de; respectively. Approximately, how many meters higher is the one than the other?a)250(1- √3)b)750(3- √3)c)250(3- √3)d)275(1- √3)Correct answer is option 'C'. Can you explain this answer?.
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