Let’s assume that the height of the tower is h meters.
We know that the angle of elevation of the top of the tower from a point at a distance of 100 meters from its foot is 60 degrees. This means that if we draw a right-angled triangle with the base as 100 meters, the angle of elevation (angle between the horizontal and the line of sight to the top of the tower) is 60 degrees. Therefore, the angle between the line of sight to the top of the tower and the vertical (i.e., the angle of depression) is also 60 degrees.
Using trigonometry, we can find the height of the tower as follows:
tan 60° = h/100
Simplifying the above equation, we get:
h = 100 x tan 60°
We know that the value of tan 60° is √3. Substituting this value in the above equation, we get:
h = 100 x √3
Therefore, the height of the tower is 100√3 meters.