Given data:

The trigonometry function is \(\displaystyle{\tan{{\left({x}\right)}}}={2}\sqrt{{{2}}}\).

Then the interval \(\displaystyle{0}^{\circ}{ < }{x}{ < }{90}^{\circ}\)

Solve the trigonometry function \(\displaystyle{\tan{{\left({x}\right)}}}={2}\sqrt{{{2}}}\)

\(\displaystyle{\tan{{\left({x}\right)}}}={2}\sqrt{{{2}}}\)

\(\displaystyle{x}={{\tan}^{{-{1}}}{\left({2}\sqrt{{{2}}}\right)}}\)

\(\displaystyle={70.528}^{\circ}\)

The trigonometry function is \(\displaystyle{\tan{{\left({x}\right)}}}={2}\sqrt{{{2}}}\).

Then the interval \(\displaystyle{0}^{\circ}{ < }{x}{ < }{90}^{\circ}\)

Solve the trigonometry function \(\displaystyle{\tan{{\left({x}\right)}}}={2}\sqrt{{{2}}}\)

\(\displaystyle{\tan{{\left({x}\right)}}}={2}\sqrt{{{2}}}\)

\(\displaystyle{x}={{\tan}^{{-{1}}}{\left({2}\sqrt{{{2}}}\right)}}\)

\(\displaystyle={70.528}^{\circ}\)