Use the axis rotation formulas:

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\left\lbrace{x}\right\rbrace}={\left\lbrace{u}\right\rbrace}{\cos{{\left\lbrace\theta\right\rbrace}}}-{\left\lbrace{v}\right\rbrace}{\sin{{\left\lbrace\theta\right\rbrace}}}\)

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\left\lbrace{y}\right\rbrace}={\left\lbrace{u}\right\rbrace}{\sin{{\left\lbrace\theta\right\rbrace}}}+{\left\lbrace{v}\right\rbrace}{\cos{{\left\lbrace\theta\right\rbrace}}}\)

From the given angle, we know that:

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\tan{{\left\lbrace\theta\right\rbrace}}}={\frac{{{5}}}{{{\left\lbrace{12}\right\rbrace}}}}\)

From this tangent ratio, opp \(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le={\left\lbrace{5}\right\rbrace}{\left\lbrace\quad\text{and}\quad\right\rbrace}{\left\lbrace{a}\right\rbrace}{\left\lbrace{d}\right\rbrace}{\left\lbrace{j}\right\rbrace}={\left\lbrace{12}\right\rbrace}\text{so}\ {\left\lbrace{h}\right\rbrace}{\left\lbrace{y}\right\rbrace}{\left\lbrace{p}\right\rbrace}=\sqrt{{{\left\lbrace{\left\lbrace{\left({\left\lbrace{o}\right\rbrace}{\left\lbrace{p}\right\rbrace}{\left\lbrace{p}\right\rbrace}\right)}\right\rbrace}^{{{2}}}+{\left\lbrace{\left({\left\lbrace{a}\right\rbrace}{\left\lbrace{d}\right\rbrace}{\left\lbrace{j}\right\rbrace}\right)}\right\rbrace}^{{{2}}}\right\rbrace}}}\)

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le=\sqrt{{{\left\lbrace{\left\lbrace{5}\right\rbrace}^{{{2}}}+{\left\lbrace{12}\right\rbrace}^{{{2}}}\right\rbrace}}}\)

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le=\sqrt{{{\left\lbrace{169}\right\rbrace}}}={\left\lbrace{13}\right\rbrace}\) so:

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\sin{{\left\lbrace\theta\right\rbrace}}}={\frac{{{\left\lbrace{\left\lbrace{o}\right\rbrace}{\left\lbrace{p}\right\rbrace}{\left\lbrace{p}\right\rbrace}\right\rbrace}}}{{{\left\lbrace{\left\lbrace{h}\right\rbrace}{\left\lbrace{y}\right\rbrace}{\left\lbrace{p}\right\rbrace}\right\rbrace}}}}={\frac{{{5}}}{{{\left\lbrace{13}\right\rbrace}}}}\)

and

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\cos{{\left\lbrace\theta\right\rbrace}}}={\frac{{{\left\lbrace{\left\lbrace{a}\right\rbrace}{\left\lbrace{d}\right\rbrace}{\left\lbrace{j}\right\rbrace}\right\rbrace}}}{{{\left\lbrace{\left\lbrace{h}\right\rbrace}{\left\lbrace{y}\right\rbrace}{\left\lbrace{p}\right\rbrace}\right\rbrace}}}}={\frac{{{12}}}{{{\left\lbrace{13}\right\rbrace}}}}\)

For x,

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\left\lbrace{x}\right\rbrace}={\left\lbrace{12}\right\rbrace}{\frac{{{u}}}{{{\left\lbrace{13}\right\rbrace}}}}-{\left\lbrace{5}\right\rbrace}{\frac{{{v}}}{{{\left\lbrace{13}\right\rbrace}}}}\)

For y,

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\left\lbrace{y}\right\rbrace}={\left\lbrace{5}\right\rbrace}{\frac{{{u}}}{{{\left\lbrace{13}\right\rbrace}}}}+{\left\lbrace{12}\right\rbrace}{\frac{{{v}}}{{{\left\lbrace{13}\right\rbrace}}}}\)

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\left\lbrace{x}\right\rbrace}={\left\lbrace{u}\right\rbrace}{\cos{{\left\lbrace\theta\right\rbrace}}}-{\left\lbrace{v}\right\rbrace}{\sin{{\left\lbrace\theta\right\rbrace}}}\)

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\left\lbrace{y}\right\rbrace}={\left\lbrace{u}\right\rbrace}{\sin{{\left\lbrace\theta\right\rbrace}}}+{\left\lbrace{v}\right\rbrace}{\cos{{\left\lbrace\theta\right\rbrace}}}\)

From the given angle, we know that:

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\tan{{\left\lbrace\theta\right\rbrace}}}={\frac{{{5}}}{{{\left\lbrace{12}\right\rbrace}}}}\)

From this tangent ratio, opp \(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le={\left\lbrace{5}\right\rbrace}{\left\lbrace\quad\text{and}\quad\right\rbrace}{\left\lbrace{a}\right\rbrace}{\left\lbrace{d}\right\rbrace}{\left\lbrace{j}\right\rbrace}={\left\lbrace{12}\right\rbrace}\text{so}\ {\left\lbrace{h}\right\rbrace}{\left\lbrace{y}\right\rbrace}{\left\lbrace{p}\right\rbrace}=\sqrt{{{\left\lbrace{\left\lbrace{\left({\left\lbrace{o}\right\rbrace}{\left\lbrace{p}\right\rbrace}{\left\lbrace{p}\right\rbrace}\right)}\right\rbrace}^{{{2}}}+{\left\lbrace{\left({\left\lbrace{a}\right\rbrace}{\left\lbrace{d}\right\rbrace}{\left\lbrace{j}\right\rbrace}\right)}\right\rbrace}^{{{2}}}\right\rbrace}}}\)

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le=\sqrt{{{\left\lbrace{\left\lbrace{5}\right\rbrace}^{{{2}}}+{\left\lbrace{12}\right\rbrace}^{{{2}}}\right\rbrace}}}\)

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le=\sqrt{{{\left\lbrace{169}\right\rbrace}}}={\left\lbrace{13}\right\rbrace}\) so:

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\sin{{\left\lbrace\theta\right\rbrace}}}={\frac{{{\left\lbrace{\left\lbrace{o}\right\rbrace}{\left\lbrace{p}\right\rbrace}{\left\lbrace{p}\right\rbrace}\right\rbrace}}}{{{\left\lbrace{\left\lbrace{h}\right\rbrace}{\left\lbrace{y}\right\rbrace}{\left\lbrace{p}\right\rbrace}\right\rbrace}}}}={\frac{{{5}}}{{{\left\lbrace{13}\right\rbrace}}}}\)

and

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\cos{{\left\lbrace\theta\right\rbrace}}}={\frac{{{\left\lbrace{\left\lbrace{a}\right\rbrace}{\left\lbrace{d}\right\rbrace}{\left\lbrace{j}\right\rbrace}\right\rbrace}}}{{{\left\lbrace{\left\lbrace{h}\right\rbrace}{\left\lbrace{y}\right\rbrace}{\left\lbrace{p}\right\rbrace}\right\rbrace}}}}={\frac{{{12}}}{{{\left\lbrace{13}\right\rbrace}}}}\)

For x,

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\left\lbrace{x}\right\rbrace}={\left\lbrace{12}\right\rbrace}{\frac{{{u}}}{{{\left\lbrace{13}\right\rbrace}}}}-{\left\lbrace{5}\right\rbrace}{\frac{{{v}}}{{{\left\lbrace{13}\right\rbrace}}}}\)

For y,

\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\left\lbrace{y}\right\rbrace}={\left\lbrace{5}\right\rbrace}{\frac{{{u}}}{{{\left\lbrace{13}\right\rbrace}}}}+{\left\lbrace{12}\right\rbrace}{\frac{{{v}}}{{{\left\lbrace{13}\right\rbrace}}}}\)