To estimate the height of a building

Question

To estimate the height of a building, two students find the angle of elevation from a point (at ground level) down the street from the building to the top of the building is 33∘. From a point that is 300 feet closer to the building, the angle of elevation (at ground level) to the top of the building is 52∘. If we assume that the street is level, use this information to estimate the height of the building.

Answer 1

tan33 = .65 = h/(300+x)

tan52 = 1.28 = h/x

(300+x).65 = h = 1.28x

1.28X- .65x = .63x =195

x = 309.5

h = tan52(309.5 = 396.2 feet

Answer 2

Let h= height

tan 33 = h/(33+X) = 0.649

tan 53 = h/X = 1.327

X = h/1.327

h/ (33+ h/1.327) = 0.649

h*1.327 = 0.649( 33+h) = 21.417 +0.649 h

gives h= 21.417/0.678

h= 31.59 ft