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An aeroplane when flying at a height of 4 4000 m from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from the same point on the ground are 60 degree and 45 degree respectively full stuff find the vertical distance between the aeroplanes at that instant . take) √ 3 is equal to 1.73)?
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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.
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An aeroplane when flying at a height of 4 4000 m from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from the same point on the ground are 60 degree and 45 degree respectively full stuff find the vertical distance between the aeroplanes at that instant . take) √ 3 is equal to 1.73)?
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