Question

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..

Answer 1

tan34°/tan30° = 1.1682
so, it has risen 16.82% in 10 minutes
At that rate, by 10:30 it will have risen by 3*16.82 = 50.46%
arctan(1.5046) = 56.4°