The Angle of Elevation of a Tower

To determine the angle of elevation of a tower at a point on the ground, we can use trigonometry. The angle of elevation is the angle between the horizontal line from the observer to the base of the tower and the line from the observer to the top of the tower.

Given:
Angle of elevation = 30°

Calculating the Height of the Tower
To calculate the height of the tower, we need to use the tangent function. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case, the opposite side is the height of the tower, and the adjacent side is the distance from the observer to the base of the tower. Let's assume this distance as "x."

Therefore, tan(30°) = height of the tower / x

Simplifying this equation, we have:
height of the tower = x * tan(30°)

Angle of Elevation with Tripled Height
If the height of the tower is tripled, then the new height would be 3 times the original height. Let's denote the new height as "3h."

Using the same formula as before, the new angle of elevation can be calculated as follows:

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

To find the new angle, we need to solve for (new angle). Rearranging the equation, we have:

(new angle) = arctan((3h) / x)

Conclusion
In conclusion, if the height of the tower is tripled, the new angle of elevation will be the arctan of three times the original height divided by the distance from the observer to the base of the tower. This calculation allows us to determine the change in the angle of elevation when the height of the tower is increased or decreased.