Question

A right triangle has base x meters and height h meters, where h is constant and x changes with respect to time t, measured in seconds. The angle θ, measured in radians, is defined by tanθ=hx. Which of the following best describes the relationship between dθdt, the rate of change of θ with respect to time, and dxdt, the rate of change of x with respect to time?


dθ/dt=(−h/x^2+h^2)dx/dt radians per second

dθ/dt=(h/x^2+h^2)dx/dt radians per second

dθ/dt=(−h/x sqrt(x^2+h^2)dx/dt radians per second

dθ/dt=(h/x sqrt(x^2+h^2)dx/dt radians per second

Answer 1

θ = arc tan ( h / x )

dθ / dx = [ arc tan ( h / x ) ]' = - h / ( x² + h² )

Answer 2

θ = arc tan ( h / x ) because tan θ = h / x

tan θ is not h x as you wrote