Hints:
The trigonometric functions are following:
[tex]\sf \sin \theta=\dfrac{opposite}{hypotenuse}\\\\\sf \cos \theta=\dfrac{adjacent}{hypotenuse} \\\\\sf \tan \theta=\dfrac{opposite}{adjacent}[/tex]
Solution:
[tex]\sf a.\quad \cos20^\circ=\dfrac{12\;m}{d}\\\\\sf{}\hspace{7.5}\quad d=\dfrac{12\;m}{\cos20^\circ} \\\\\sf{}\hspace{7.5}\quad d=12.77\;m\quad (ANSWER)[/tex]
[tex]\sf b.\quad \tan\theta=\dfrac{12\;m}{14\;m}\\\\\sf{}\hspace{7.5}\quad \theta=\tan^{-1}\left(\dfrac{12\;m}{14\;m}\right) \\\\\sf{}\hspace{7.5}\quad \theta=40.6^\circ\quad (ANSWER)[/tex]
[tex]\sf c.\quad \cos30^\circ=\dfrac{v_x}{v}\\\\\sf{}\hspace{7.5}\quad v_x=v\cos 30^\circ \\\sf{}\hspace{7.5}\quad v_x=(52\;m/s)(\cos 30^\circ)\\\sf{}\hspace{7.5}\quad v_x=45.03\;m/s\quad (ANSWER)\\\\and\\\\\sf{}\hspace{15}\sin30^\circ=\dfrac{v_y}{v}\\\\\sf{}\hspace{7.5}\quad v_y=v\sin 30^\circ \\\sf{}\hspace{7.5}\quad v_y=(52\;m/s)(\sin 30^\circ)\\\sf{}\hspace{7.5}\quad v_y=26\;m/s\quad (ANSWER)[/tex]
[tex]\sf d.\quad \tan\theta=\dfrac{v_y}{v_x}\\\\\sf{}\hspace{7.5}\quad \tan\theta=\dfrac{12\;m/s}{8\;m/s}\\ \\\sf{}\hspace{7.5}\quad \theta=\tan^{-1}\left(\dfrac{12\;m/s}{8\;m/s}\right)\\\\\sf{}\hspace{7.5}\quad \theta=56.3^\circ\quad(ANSWER)\\\\and\\\\\sf{}\hspace{15}\sin(56.3^\circ)=\dfrac{v_y}{v}\\\\\sf{}\hspace{7.5}\quad v=\dfrac{v_y}{\sin(56.3^\circ)} \\\\\sf{}\hspace{7.5}\quad v=\dfrac{12\;m/s}{\sin(56.3^\circ)} \\\\\sf{}\hspace{7.5}\quad v=14.42\;m/s\quad (ANSWER)[/tex]
