Answer
$27^{\circ}$
Work Step by Step
The maximum force occurs when the current is perpendicular to the magnetic field, and the sine of the angle is 90 degrees. See equation 20-2.
Here, $\frac{F}{\mathcal{l}}=0.45\frac{F_{max}}{\mathcal{l}}$
Use equation 20-1 and solve for the force per meter.
$$\frac{F}{\mathcal{l}}=IBsin\theta=0.45IB$$
$$\theta=sin^{-1}0.45 = 27^{\circ}$$