An ant looks to the top of a bulding at an angle of elevation of 32°. The ant then walks an additional 66 feet from the edge of
the building. If the new angle of elevation from the ant to the top of the building is 22°, find the height of the building. Round to the nearest tenth
Let the height of the building be x. Let the initial distance of the ant from the building be y, then tan 32 = x/y y = x/tan 32 . . . . . . . . (1) tan 22 = x/(y + 66) y tan 22 + 66 tan 22 = x y = (x - 66 tan 22)/tan 22 . . . . . . . . (2) Equating (1) and (2), we have x/tan 32 = (x - 66 tan 22)/tan 22 x tan 22 = x tan 32 - 66 tan 22 (tan 32) x(tan 32 - tan 22) = 66 tan 22 (tan 32) x = (66 tan 22 (tan 32))/(tan 32 - tan 22) = 66(0.4040)(0.6249)/(0.6249 - 0.4040) = 16.6626/0.2208 = 75.4
Therefore, the height of the building is 75.4 feet.
