From the top of a building 60 feet high, the angle of elevation of the top of a pole is 14 degrees. At the bottom of the building the angle of elevation of the top of the pole is 28 degrees. Find the distance from the pole to the building.
Let h be the height of the pole and d be the distance from the building.
tan(28) = h/d ...(1)
tan(14) = (h-60)/d ...(2)
Rewrite (2) as tan(14) = h/d - 60/d ...(3)
Use (1) in (3): tan(14) = tan(28) - 60/d ...(4)
Rearrange (4) to get d = 60/(tan(28)-tan(14))
d=60(tan360∘(28∘)−tan360∘(14∘))⇒d=212.4785622452215097
or d ≈ 212.5 ft
Let h be the height of the pole and d be the distance from the building.
tan(28) = h/d ...(1)
tan(14) = (h-60)/d ...(2)
Rewrite (2) as tan(14) = h/d - 60/d ...(3)
Use (1) in (3): tan(14) = tan(28) - 60/d ...(4)
Rearrange (4) to get d = 60/(tan(28)-tan(14))
d=60(tan360∘(28∘)−tan360∘(14∘))⇒d=212.4785622452215097
or d ≈ 212.5 ft