To find \(\cos^2(27^\circ)\), you can first calculate \(\cos(27^\circ)\) and then square the result.
Using a calculator or trigonometric tables:
\[ \cos(27^\circ) \approx 0.848 \]
Now, squaring this value:
\[ \cos^2(27^\circ) \approx (0.848)^2 \approx 0.719 \]
So, \(\cos^2(27^\circ) \approx 0.719\). If you require a more precise value, please use a scientific calculator or software capable of high-precision calculations.