Question

a person who eyes are 5 feet above the ground observes the top of a building to have an angle of elevation of 40 degree. The person walks 100 feet closer to the building and observes that the top of the building now has an angle of elevation of 65 degree. How high is the building?

Answer 1

Let the height of the building be h; let the man start at distance x from the building.

(h-5)/x = tan40 = 0.839
(h-5)/(x-100) = tan60 = 1.732

h = 167.7 ft
x = 193.9 ft

check:
162.7/193.9 = 0.839
162.7/93.9 = 1.732