need help on calculus problem: A ballon leaves the ground 500 feet away from an observer and rises vertically at the rate of 140 feet per minute. At what rate is the angle of inclination of the observer's line of sight increasing at the instant when the balloon is exactly 500 feet above the ground?

Question

experimentx · Answer

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$ \tan \theta = h/b$ b is constant
differentiate both
sex^2 θ dθ/dt = dh/dt * 1/b
dθ/dt = dh/dt * 1/b cos^2 θ = dh/dt * 1/b * b/sqrt(b^2+h^2)