A hot air balloon rising straight up from a level field is track by a range finder 500 ft from the point of lift off.

$\dfrac{dy}{dt} = 500 \sec^2 \theta \cdot \dfrac{d\theta}{dt}$

$\dfrac{dy}{dt} = \dfrac{500}{\cos^2 \theta} \cdot \dfrac{d\theta}{dt}$
 

When θ = 45°,   dθ/dt = 0.14

$\dfrac{dy}{dt} = \dfrac{500}{\cos^2 45^\circ} \cdot 0.14$

$\dfrac{dy}{dt} = 140 ~ \text{ft/min}$

Set the angle of your calculator into RAD
$\dfrac{dy}{dt} = \dfrac{d}{dt}\Big( 500 \tan \theta \Big)_{\theta = 45^\circ ~ \times ~ \pi/180^\circ} \cdot \dfrac{d\theta}{dt}$

$\dfrac{dy}{dt} = 1000 \cdot 0.14$

$\dfrac{dy}{dt} = 140 ~ \text{ft/min}$