\(\displaystyle{40}'=\frac{{40}}{{60}^{\circ}}\)

\(\displaystyle=\frac{{2}}{{3}^{\circ}}\)

Use the tangent ratio:

\(\displaystyle{\tan{\angle}}=\frac{{{o}{p}{p}}}{{{a}{d}{j}}}\)

Let the adj. side be x. Substitute the given:

\(\displaystyle{{\tan{{\left(\frac{{2}}{{3}}\right)}}}^{\circ}=}\frac{{75}}{{x}}\)

\(\displaystyle{x}=\frac{{75}}{{{\tan{{\left(\frac{{2}}{{3}}\right)}}}^{\circ}}}\)

\(\displaystyle{x}\approx{6445.5}{m}\)

\(\displaystyle=\frac{{2}}{{3}^{\circ}}\)

Use the tangent ratio:

\(\displaystyle{\tan{\angle}}=\frac{{{o}{p}{p}}}{{{a}{d}{j}}}\)

Let the adj. side be x. Substitute the given:

\(\displaystyle{{\tan{{\left(\frac{{2}}{{3}}\right)}}}^{\circ}=}\frac{{75}}{{x}}\)

\(\displaystyle{x}=\frac{{75}}{{{\tan{{\left(\frac{{2}}{{3}}\right)}}}^{\circ}}}\)

\(\displaystyle{x}\approx{6445.5}{m}\)