an air balloon is 80ft away from you with the angle of elevation of the rising balloon changing at a rate of 4 degrees per second how fast is the balloon rising when it is 6 feet off the ground.

Answer 1

assuming the 80 ft is along the ground,
h/80 = tanθ
1/80 dh/dt = sec^2θ dθ/dt
when h=6, sec^2θ = 1+tan^2θ = 1+(6/80)^2 = 1.0056

1/80 dh/dt = 1.0056 * 4*π/180
dh/dt = 5.6 ft/s