Let d be the difference in the height of the two buildings.

Let y bet the height of the flagpole.

Let P be the point on the lower building.

x = the distance from the edge of the taller building to point P.

By opposite angles of parallel lines, the elevation angle from point P to the top of the flag pole is B°=54°.

tan(54°) = (y+d)/x --> y+d = 1660 tan(54°) = 2284.8 ft

By opposite angles of parallel lines, the elevation angle from point P to the bottom of the flag pole is A°=41°.

d/x = tan(41°) --> d = 1660tan(41°) = 1443 ft

y = 2284.8 -d = 2284.8-1443 = 841.8 ft.

height of flagpole = 841.8 feet