17. A bird sits on top of a lamppost. The angle made by the lamppost and a line from the feet of the bird to the feet of an observer standing away from the lamppost is $55^{\circ}$. The distance from the lamppost to the observer is 25 feet. Estimate the height of the lamppost?

Step 1 ：Given that the angle made by the lamppost and a line from the feet of the bird to the feet of an observer standing away from the lamppost is \(55^{\circ}\). The distance from the lamppost to the observer is 25 feet. We are asked to estimate the height of the lamppost.

Step 2 ：We can use trigonometry to solve this problem. Specifically, we can use the tangent of the angle, which is the ratio of the opposite side (the height of the lamppost) to the adjacent side (the distance from the lamppost to the observer).

Step 3 ：So, we can set up the equation \(\tan(55) = \frac{height}{25}\) and solve for height.

Step 4 ：Converting the angle to radians, we get \(55^{\circ} = 0.9599310885968813\) radians.

Step 5 ：Solving the equation for height, we get \(height = 25 \times \tan(0.9599310885968813) = 35.70370016855286\) feet.

Step 6 ：Final Answer: The height of the lamppost is approximately \(\boxed{35.7}\) feet.