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 37°

Question

From a point that is 350 feet closer to the building, the angle of elevation (at ground level) to the top of

the building is 55°. If we assume that the street is level, use this information to estimate the height of the building.

The height of the building is ____ feet 

Answer 1

Let x = the distance from where the angle is 55 to the top of the building

Let h= the height of the building

then tan55 = h/x = 1.428

and tan37 = h/(x+350) = 0.754

you have 2 equations 2 unknowns

1.438x = h

0.754(x+350) = h

1.438x = 0.754x + 263.7

0.684x = 263.7

x = 263.7/.684 = 385.5

h=1.438(385.5) = 554.4 feet is the height of the building