For the amusement of the guests some hotels have elevators o

For the amusement of the guests, some hotels have elevators on the outside of the building. One such hotel is 200 feet high. You are standing by a window 100 feet above the ground and 150 feet away from the hotel, and the elevator descends at a constant speed of 20 ft/sec, starting at time t = 0, where t Is time In seconds. Let theta be the angle between the line of your horizon and your line of sight to the elevator. Find a formula for h(t), the elevator\'s height above the ground as It descends from the top of the hotel. Using your answer to part (a), express theta as a function of time t.

Solution

After t seconds, the elevator has descended 20t feet. If it started at a height of 200 feet, its current height ,
h(t) = 200 - 20t
b)
h - 100 is the elevator\'s height above you
Assuming theta is the angle of the elevator\'s height ABOVE you, i.e. if theta is positive, the elevator is HIGHER than you:
tan(theta) = (h - 100) / 150
tan(theta) = (200 - 20t - 100) / 150
tan(theta) = (100 - 20t) / 150
tan(theta) = (10 - 2t) / 15
theta = arctan((10 - 2t) / 15).