A balloon is rising vertically 150 m from an observer. At exactly 1 min, the angle of elevation is 29 deg 28 min. How fast is the balloon rising at that instant?

Answer 1

Draw the diagram, and you will note that when the balloon is at height h,
h/150 = tanθ
That means that
1/150 dh/dt = sec^2θ dθ/dt
dh/dt =150 sec^2(29°28') dθ/dt
See what you can do with that.