#### Answer

Airplanes bank when they turn so that the lift force generated by the wings has a horizontal component, which the plane requires to move in a horizontal circle.
The required angle can be calculated by $\theta = tan^{-1}(\frac{gr}{v^{2}})$.

#### Work Step by Step

The way to calculate the banking angle is as follows. See the diagram.
The lift force’s vertical component balances the plane’s weight.
$$F_{L}sin \theta = mg$$
The horizontal component provides the necessary centripetal force.
$$F_{L}cos \theta = m \frac{v^{2}}{r}$$
By dividing the two equations and solving, we can find the required bank angle.
$$\theta = tan^{-1}(\frac{gr}{v^{2}})$$