A hot-air balloon is rising vertically at a constant speed, an observer at a distant observes the elevation angle to be 30° at 10:00am, at 10:10am the elevation angle becomes 34°, then at 10:30am the elevation angle of the balloon should be closest to (using the table below) (A) 34° (B) 39° (C) 41° (D) 42° (E) 43°
If the observer is x ft from the spot below the balloon,
h = height at 10:00
s = height at 10:10
h/x = tan30°
s/x = tan34°
so
h/tan30 = s/tan34
s = h tan34°/tan30° = 1.168h
at 10:30 the height will be 1.505h
1.505tan30° = tan40.98°
so I guess C is the best choice.