Answer
$\theta_2 = 43.2^{\circ}$
Work Step by Step
We can write an expression for the angles of the diffraction orders:
$sin~\theta_m = \frac{m~\lambda}{d}$
We can find the value of $\frac{\lambda}{d}$:
$sin~\theta_1 = \frac{(1)~\lambda}{d}$
$\frac{\lambda}{d} = sin~20.0^{\circ}$
$\frac{\lambda}{d} = 0.342$
We can find the angle of the second order maximum:
$sin~\theta_2 = \frac{(2)~\lambda}{d}$
$sin~\theta_2 = (2)(0.342)$
$sin~\theta_2 = 0.684$
$\theta_2 = sin^{-1}~(0.684)$
$\theta_2 = 43.2^{\circ}$
