the distance from you to the base of a tower on top of a hill is 2760 ft. the angle of elevation of the base is 26 degrees the angle of elevation of the top of the tower is 32 degrees.find the nearest foot the height of the tower above the top of the hill

Answer 1

the angle of declination from the top is 32, so the angle between the line of sight to you and the tower is 58 deg.
so now, in the upper triangle, you have SAA
law of sines:
2760/sin58=h/sin4
solve for h. I get about a little less than 230 ft.

Answer 2

h1 = 2760*Tan26 = 1346 Ft. = Ht. of hill above gnd.,
h2 = Ht. of tower above top of hill,
h1+h2 = 2760*Tan32,
h2 = 2760*Tan32 - h1 = 1725 - 1346 = 379 Ft.