From a balloon 1191 feet high, the angle of depression to the ranger headquarters is 72°54'. how far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)

Since angle of depression = 72°54 minutes.

60 minutes = 1°

54 minutes = 54/60 = 0.9°

Therefore  72°54 minutes =  72° + 0.9° = 72.9°

Since angle of depression =  72.9°,   the reverse angle of elevation =  72.9°

(Picture representation of this using right angled triangle is needed)

tan  72.9° =   Opposite height / Horizontal distance

tan 72.9° = 1191 / x

x = 1191 / tan 72.9               Use a calculator.

x ≈1191 / 3.2506

x ≈ 366.39

Horizontal distance ≈ 366.39 feet.

Hope this helped.