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An airplane flying at 3000 m above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 60º and 45º respectively. The height of the lower plane from the ground is:?
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An airplane flying at 3000 m above the ground passes vertically above ...
Understanding the Problem
To find the height of the lower plane from the ground, we need to analyze the situation using the angles of elevation from a point on the ground.
Given Data
- Height of the upper plane (Plane 1): 3000 m
- Angle of elevation of Plane 1: 60º
- Angle of elevation of Plane 2 (lower plane): 45º
Using Trigonometry
1. Calculating the Distance to Plane 1:
- From the angle of elevation (60º), we can use the tangent function:
- tan(60º) = height / distance
- tan(60º) = √3, so:
- √3 = 3000 m / distance to Plane 1
- Distance to Plane 1 = 3000 / √3 m
2. Calculating the Height of Plane 2:
- From the angle of elevation (45º), we use the tangent function again:
- tan(45º) = height of Plane 2 / distance to Plane 2
- tan(45º) = 1, thus:
- Height of Plane 2 = distance to Plane 2
3. Equating Distances:
- Since both planes are observed from the same point, the distances to both planes must be equal:
- Distance to Plane 1 = Distance to Plane 2
- Therefore, we have:
- 3000 / √3 = height of Plane 2
Final Calculation
- To find the height of Plane 2:
- Height of Plane 2 = 3000 / √3 ≈ 1732.05 m
Conclusion
The height of the lower plane from the ground is approximately 1732.05 meters.
To find the height of the lower plane from the ground, we need to analyze the situation using the angles of elevation from a point on the ground.
Given Data
- Height of the upper plane (Plane 1): 3000 m
- Angle of elevation of Plane 1: 60º
- Angle of elevation of Plane 2 (lower plane): 45º
Using Trigonometry
1. Calculating the Distance to Plane 1:
- From the angle of elevation (60º), we can use the tangent function:
- tan(60º) = height / distance
- tan(60º) = √3, so:
- √3 = 3000 m / distance to Plane 1
- Distance to Plane 1 = 3000 / √3 m
2. Calculating the Height of Plane 2:
- From the angle of elevation (45º), we use the tangent function again:
- tan(45º) = height of Plane 2 / distance to Plane 2
- tan(45º) = 1, thus:
- Height of Plane 2 = distance to Plane 2
3. Equating Distances:
- Since both planes are observed from the same point, the distances to both planes must be equal:
- Distance to Plane 1 = Distance to Plane 2
- Therefore, we have:
- 3000 / √3 = height of Plane 2
Final Calculation
- To find the height of Plane 2:
- Height of Plane 2 = 3000 / √3 ≈ 1732.05 m
Conclusion
The height of the lower plane from the ground is approximately 1732.05 meters.
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An airplane flying at 3000 m above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 60º and 45º respectively. The height of the lower plane from the ground is:?
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An airplane flying at 3000 m above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 60º and 45º respectively. The height of the lower plane from the ground is:? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about An airplane flying at 3000 m above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 60º and 45º respectively. The height of the lower plane from the ground is:? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An airplane flying at 3000 m above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 60º and 45º respectively. The height of the lower plane from the ground is:?.
An airplane flying at 3000 m above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 60º and 45º respectively. The height of the lower plane from the ground is:? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about An airplane flying at 3000 m above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 60º and 45º respectively. The height of the lower plane from the ground is:? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An airplane flying at 3000 m above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 60º and 45º respectively. The height of the lower plane from the ground is:?.
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