Question

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

Answer 1

no choices given, but you have
tanθ = h/x = 1/x * h
so, taking the derivative of both sides (remember, x is just a constant)
sec^θ dθ/dt = 1/x dh/dt

Answer 2

The answer they was looking for is
A. dθ/dt = ( x/x^2+h^2) dh/dt radians per second