From the top of a tower h meters high, the angles of depression of two objects, which are in line with the foot of the tower, are alpha and beta (where beta > alpha). We need to find the distance between the two objects.


To solve this problem, we will use the concept of trigonometry and right-angled triangles.


Let's start by drawing a diagram to visualize the situation. We have a tower with height h, and two objects at some distances from the foot of the tower. We can represent the tower as a vertical line and the objects as points on the ground.


From the problem statement, we know the following:
- The height of the tower is h meters.
- The angles of depression of the two objects are alpha and beta, where beta > alpha.


Now, let's apply trigonometry to find the distance between the two objects.

We can consider the right-angled triangle formed by the tower, one of the objects, and the foot of the tower. The angle of depression (alpha) is the angle between the line of sight from the top of the tower to the object and the horizontal ground.

Using trigonometry, we can say:
tan(alpha) = h / x1, where x1 is the distance between the foot of the tower and the first object.

Similarly, for the second object:
tan(beta) = h / x2, where x2 is the distance between the foot of the tower and the second object.


We need to find the distance between the two objects, which is x2 - x1.

To calculate this, we need to eliminate x1 and x2 from the above equations. We can do this by solving the equations simultaneously.

Divide the equation tan(beta) = h / x2 by tan(alpha) = h / x1:
(tan(beta) / tan(alpha)) = (h / x2) / (h / x1)
(tan(beta) / tan(alpha)) = (x1 / x2)

Now, rearrange the equation to isolate x2:
x2 = (x1 * tan(beta)) / tan(alpha)

Finally, substitute this value of x2 in the equation x2 - x1 to find the distance between the two objects.


To simplify the equation further, we can substitute the values of tan(alpha) and tan(beta) with their respective angles using a scientific calculator.


Substitute the values of x1, tan(alpha), tan(beta), and h in the equation x2 - x1 to find the distance between the two objects.


The final answer is the distance between the two objects, obtained from the calculation in step 6.

In this way, we can find the distance between two objects when the angles of depression from the top of a tower are known.