Answer :
Final answer:
The height of the antenna is approximately 105 feet.
Explanation:
To find the height of the antenna, we can use trigonometry. Let's assume the height of the antenna is h.
Using the first observation, we can form a right triangle with the height of the antenna as the opposite side and the distance between the observer and the antenna as the adjacent side. The tangent of the angle of elevation is equal to the opposite side divided by the adjacent side:
tan(53) = h / x
where x is the initial distance between the observer and the antenna.
Similarly, using the second observation, we can form another right triangle with the new distance between the observer and the antenna as the adjacent side and the height of the antenna as the opposite side:
tan(29) = h / (x + 59)
We can now solve these two equations simultaneously to find the height of the antenna, h, which is approximately 105 feet.
