Well, trigonometry can be a bit tricky sometimes, but don't worry, I'm here to help you out!
In this particular scenario, using the tangent function to find the rate at which the angle of elevation is changing makes the most sense because we have the ratio of the height to the distance. The tangent function is defined as the ratio of the opposite side (in this case, the altitude) to the adjacent side (the distance).
The derivative of the tangent function is indeed the correct way to find this rate. However, it's important to note that the other trigonometric functions (sine and cosine) would not give you the same information in this case.
Sine and cosine functions are useful for calculating the side lengths in a right triangle, given an angle and one of the sides. They can also be used to find the rate at which the side lengths are changing, but in this problem, we are specifically asked about the angle of elevation.
So, in this case, it's not that only one trig function would work to solve the problem, but rather choosing the appropriate trig function based on the information given and what you're trying to find. In this scenario, the tangent function is the most suitable choice.
I hope that clears things up a bit! Let me know if you have any more questions or if there's anything else I can help you with.