A six feet tall man looks out a fifth story window of a hotel. He sees a statue that is 75 ft away from the hotel. If he is looking at the base of the statue, what angle does his sight line form with the side of the hotel? Assume that each complete story of the hotel is 12 ft tall.

32.6

43.9

48.7

54.2

Distance from the base of the hotel to the base of the statue = 75ft

Height of the position of the man is (4 x 12) + 6 = 48 + 6 = 54 ft [since each complete story of the hotel is 12 ft tall, the man is on the fifth stort means that there are 4 complete stories plus the height of the man]

Let the require angle be x, the side opposite the angle is the horizontal distance from the base of the hotel to the base of the statue and the side adjacent the angle is the vertical height of the position of the man.

Thus, tan x = opposite / adjacent = 75 / 54 = 1.3889

x = tan^-1 (1.3889) = 54.2 ft