Question

Benjamin is observing a hotel's entrance from a bench 30ft away. Write a function to model the height h of the hotel as a function of the angle of inclination x from his position to the entrance of the hotel

Answer 1

To model the height h of the hotel as a function of the angle of inclination x from Benjamin's position to the entrance of the hotel, you can use trigonometry. The function to model the height is h(x) = 30 * cos(x).

Step-by-step explanation:

To model the height h of the hotel as a function of the angle of inclination x, we can use trigonometry. The angle x can be thought of as the angle of elevation from Benjamin's position to the entrance of the hotel. Let's consider a right triangle formed by Benjamin, the entrance of the hotel, and a point on the ground directly below Benjamin. The length of this triangle's hypotenuse is the distance between Benjamin and the hotel entrance, which is 30 ft.

Using the trigonometric relationship cosine, we have cos(x) = adjacent/hypotenuse. In this case, the adjacent side is the height of the hotel (h) and the hypotenuse is 30 ft. Solving for h, we get h = 30 ft * cos(x).

Therefore, the function to model the height h of the hotel as a function of the angle of inclination x is: h(x) = 30 * cos(x).