**Angle of Elevation and Height of the Tower**

The angle of elevation is a geometric term that refers to the angle between the horizontal line of sight and the line of sight from the observer to the top of an object. In this case, we are given that the angle of elevation of the top of a tower is 30° at a point on the ground.

The height of the tower can be determined by using trigonometric principles. By considering a right triangle formed by the observer, the tower, and the line of sight, we can use the tangent function to find the height.

Let's assume that the distance from the observer to the tower is represented by "d" and the height of the tower is represented by "h". Using the tangent function, we can write:

tan(30°) = h/d

Simplifying this equation, we have:

h = d * tan(30°)

**Tripling the Height of the Tower**

Now, let's consider what happens when the height of the tower is tripled. If the original height of the tower is "h", then the new height would be 3h.

To find the new angle of elevation, we need to determine the new distance from the observer to the tower. Let's assume this new distance is represented by "d'".

We can use the same trigonometric principles as before to find the new angle of elevation. Using the tangent function, we can write:

tan(new angle) = (3h) / d'

To find the relationship between "d'" and "d", we can use similar triangles. The triangles formed by the observer, the tower, and the line of sight are similar. This means that the ratio of corresponding sides is the same.

In this case, the ratio of the height to the distance (h/d) remains constant. So, we can write:

h/d = (3h) / d'

Simplifying this equation, we find:

d' = d/3

**Calculating the New Angle of Elevation**

Now, we can substitute the value of d/3 into the equation for the tangent of the new angle of elevation:

tan(new angle) = (3h) / (d/3)

tan(new angle) = 9h / d

Since we know that tan(30°) = h/d, we can substitute this value into the equation:

tan(new angle) = 9(tan(30°))

Using a calculator, we can determine the value of tan(30°) and calculate the new angle of elevation.

By following these steps, we can determine the new angle of elevation when the height of the tower is tripled.