the angle of elevation of the top of the tower standing on a Horizontal plane from a pont A is α and after walking distance d towards it the amgle of elevation is β the height of tower is

To solve this problem, we will use the concept of trigonometry. Here are the steps:

1. From point A, the angle of elevation to the top of the tower is α. So, we can form a right triangle with the tower as one side, the line from point A to the base of the tower as another side, and the line of sight to the top of the tower as the hypotenuse. Let's denote the height of the tower as h and the distance from point A to the tower as x. Then, tan(α) = h/x.

2. After walking a distance d towards the tower, the angle of elevation becomes β. Now, the distance from the point to the tower is (x-d). Again, we can form a right triangle with the tower as one side, the line from the new point to the base of the tower as another side, and the line of sight to the top of the tower as the hypotenuse. Then, tan(β) = h/(x-d).

3. Now we have a system of two equations, and we can solve it for h:

   From tan(α) = h/x, we get h = x*tan(α) ...(equation 1)

   And from tan(β) = h/(x-d), we get h = (x-d)*tan(β) ...(equation 2)

4. Since the height of the tower remains the same, we can equate the right sides of equation 1 and equation 2:

   x*tan(α) = (x-d)*tan(β)

5. Solve this equation for x:

   x = d*tan(β) / (tan(α) - tan(β))

6. Substitute x in equation 1 or equation 2 to find h:

   h = d*tan(α)*tan(β) / (tan(α) - tan(β))

So, the height of the tower is d*tan(α)*tan(β) / (tan(α) - tan(β)).