Question

Solve for theta please!

Answer 1

$\bf mg sin(\theta )=\mu mg cos(\theta )\implies \cfrac{~~\begin{matrix} mg \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ sin(\theta )}{~~\begin{matrix} mg \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ cos(\theta )}=\mu\implies tan(\theta )=\mu \\\\\\ tan^{-1}\left[ tan(\theta ) \right]=tan^{-1}(\mu)\implies \theta=tan^{-1}(\mu)$