Hight 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 . From a point that is 400 feet closer to the building, the angle of elevation (at ground level) to the top of the building is . 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 the initial distance to the bottom of the building = 400 + x

x= distance from 2nd position to bottom of the building

let h= height of the building

construct some right triangles, one with angle 39 base x, the other with angle 48 base 400+x

tan48= h/(x),

tan39 = h/(x+400)

h= xtan48 = (x+400)tan39

xtan48 = 400tan39 +xtan39

x(tan48-tan39)= 400tan39

then x = 400tan39/(tan48-tan39) = 400(.81)/.3 =324/.3 = 1080

height of the building = 1080tan48 = 1080(1.11)=about 1198.8 feet + or - about 3, rounded off

h = exactly tan48(400tan39)/(tan48-tan39)

cary as many decimal places as you want accuracy