Explanation

(c)
Given, $\overrightarrow{\mathbf{a}}\mathbf{+}\overrightarrow{\mathbf{b}}\mathbf{+}\overrightarrow{\mathbf{c}}\mathbf{=}\overrightarrow{\mathbf{0}}$ and $\left| \overrightarrow{\mathbf{a}} \right| = \sqrt{37},\ \left| \overrightarrow{\mathbf{b}} \right| = 3,\ and\ \left| \overrightarrow{\mathbf{c}} \right| = 4$
Now, $\overrightarrow{\mathbf{a}}\mathbf{+}\overrightarrow{\mathbf{b}}\mathbf{+}\overrightarrow{\mathbf{c}}\mathbf{=}\overrightarrow{\mathbf{0}}$
$\Rightarrow \ \overrightarrow{\mathbf{a}}\mathbf{= -}\left( \overrightarrow{\mathbf{b}}\mathbf{+}\overrightarrow{\mathbf{c}} \right)\$
$\Rightarrow \left| \overrightarrow{\mathbf{a}} \right|^{2} = \left| \ - \left( \overrightarrow{\mathbf{b}}\mathbf{+}\overrightarrow{\mathbf{c}} \right) \right|^{2}$
$\Rightarrow \ \left| \overrightarrow{\mathbf{a}} \right|^{2} = \left| \overrightarrow{\mathbf{b}} \right|^{2} + \left| \overrightarrow{\mathbf{c}} \right|^{2} + 2\left| \overrightarrow{\mathbf{b}} \right|\left| \overrightarrow{\mathbf{c}} \right|\cos\theta$
$= 9 + 16 + 24\cos\theta$
$\Rightarrow 37 = 25 + 24\cos\theta$
$\Rightarrow 24\cos{\theta = 12\ \Rightarrow \ \theta = 60{^\circ}}$