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Level Finder

Level Finder
Level Finder
related rates math problem?

A hot air balloon rising straight up from a level field is tracked by a range finder 500ft from the lift point. At the moment the range finder's elevation angle is π/4, the angle is increasing at the rate of 0.14 rad/min. How fast is the balloon rising at the moment.

I've only been able to find the equation which is
tan feta= x/500

please show your work

tan(θ) = x/500
sec²(θ) dθ = dx/500
dx/dθ = 500 sec²(θ)

dx/dt = dx/dθ dθ/dt .......... chain rule ; dθ/dt given as 0.14 radians/min
dx/dt = 500 sec²(π/4) (0.14)
= 140 ft/min

Answer: 140 ft/min

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