••••••the height of the tower is 30m and the distance from its foot is 10√3 it means .... P= 30 m and B = 10√3m and u know that tan(theta) = P/B .... put the value of P and B in the above relation and the answer will be 60 degree•••••••

The angle of elevation of the sun can be determined by using the concept of similar triangles. Let's break down the problem and solve it step by step.

Given Information:
- Height of the tower = 30 meters
- Length of the shadow cast by the tower = 10√3 meters

Understanding the Problem:
We need to find the angle of elevation of the sun. The angle of elevation is the angle between the ground and the line of sight from the observer to the sun.

Step 1: Draw a Diagram
To better visualize the problem, let's draw a diagram. Draw a vertical line to represent the tower and a horizontal line to represent the ground. Label the height of the tower as 30 meters and the length of the shadow as 10√3 meters.

Step 2: Identify Similar Triangles
In the diagram, we can see two triangles: the triangle formed by the tower, its shadow, and the ground, and the triangle formed by the tower and the line of sight to the sun.

Step 3: Apply Similar Triangles
Since the two triangles are similar, we can set up a proportion to find the angle of elevation. The ratio between the height of the tower and the length of its shadow should be equal to the ratio between the height of the tower and the distance from the observer to the sun.

Let's denote the angle of elevation as θ.

Using the given information, we can set up the proportion as follows:

30 / (10√3) = 30 / d

Simplifying the equation:

1 / (√3) = 1 / d

Cross-multiplying:

d = √3

Step 4: Find the Angle of Elevation
The value of d represents the distance from the observer to the sun. Since the distance between the observer and the sun is extremely large compared to the height of the tower, we can assume that the distance is practically infinite.

Therefore, the angle of elevation can be calculated using the tangent function:

tan(θ) = (30 / d)

tan(θ) = (30 / √3)

θ = arctan(30 / √3)

Using a calculator, we can determine that the angle of elevation θ is approximately 60 degrees.

Conclusion:
The angle of elevation of the sun is approximately 60 degrees. This means that the sun is positioned 60 degrees above the horizon when the tower casts a shadow of 10√3 meters on the ground.