I'm doing some Engineering Mechanics homework regarding equilibrium of rigid bodies and I've come across a problem involving radians that has stomped me. I have the question and the steps to find the answer in the image attachments, but I don't understand how they figured out how to find the radians. I would try and type out the steps they took but it wouldn't make sense without seeing the image in the question.
I have to find the angle that the rod makes from the horizontal so that the rod is in equilibrium. There's a linear torsional spring that deforms, applying a couple moment $ M $ related to the spring's rotation $ \theta $ in radians: $ M=40\theta\ {N\cdot m} $. There's also the gravitational force acting in the center of the rod. Whenever I used the equation to sum the moments to zero, I got stuck.
$$ \Sigma \, M_{A}\, = \, (245.25 \: N)(cos(\theta \cdot\frac{180}{\pi} ))(0.25 \:m)\, + \, 40\theta\, N\! \cdot\! m = 0 $$
I can't figure out how I'm supposed to solve for $ \theta $ if it is both inside and outside the cosine. Here is the solution I found, but it didn't help me.
If anyone could help explain how the final answer can be found I'd greatly appreciate it. Thanks in advance!