An aeroplane when flying at a height of 4 4000 m from the ground passe...
Vertical Distance between Two Aeroplanes
Given Information
- The height of the first aeroplane from the ground is 4,000 m.
- The angle of elevation of the first aeroplane from a point on the ground is 60 degrees.
- The angle of elevation of the second aeroplane from the same point on the ground is 45 degrees.
- The value of √3 is 1.73.
Calculating the Vertical Distance
To find the vertical distance between the two aeroplanes, we can use trigonometry.
Step 1: Finding the Horizontal Distance
Let's assume that the distance between the two aeroplanes on the ground is 'x' meters.
From the given information, we can form the following equations:
- Tan 60° = height of the first aeroplane / x
- Tan 45° = height of the second aeroplane / (x + vertical distance)
Simplifying these equations, we get:
- √3 = 4000 / x
- 1 = (4000 + vertical distance) / x
Step 2: Solving the Equations
We can solve the above equations simultaneously to find the value of 'x' and the vertical distance between the two aeroplanes.
Multiplying the first equation by x and the second equation by 4000 + vertical distance, we get:
- √3x = 4000
- 4000 + vertical distance = x
Substituting the value of x from the first equation into the second equation, we have:
- 4000 + vertical distance = √3x
- 4000 + vertical distance = √3 * 4000
- 4000 + vertical distance = 1.73 * 4000
- 4000 + vertical distance = 6920
Solving for vertical distance, we get:
- vertical distance = 6920 - 4000
- vertical distance = 2920 m
Answer
The vertical distance between the two aeroplanes at that instant is 2,920 meters.