Step 1: Recall standard trigonometric values
From the trigonometric table:
\[
\cos 0^\circ = 1,\ \cos 30^\circ = \frac{\sqrt{3}}{2},\ \cos 45^\circ = \frac{1}{\sqrt{2}},\ \cos 60^\circ = \frac{1}{2},\ \cos 90^\circ = 0
\]
Step 2: Apply for $\cos 60^\circ$
Clearly, \[
\cos 60^\circ = \frac{1}{2}
\]
\[
\boxed{\cos 60^\circ = \tfrac{1}{2}}
\]
Find the unknown frequency if 24 is the median of the following frequency distribution:
\[\begin{array}{|c|c|c|c|c|c|} \hline \text{Class-interval} & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 \\ \hline \text{Frequency} & 5 & 25 & 25 & \text{$p$} & 7 \\ \hline \end{array}\]
Two concentric circles are of radii $8\ \text{cm}$ and $5\ \text{cm}$. Find the length of the chord of the larger circle which touches (is tangent to) the smaller circle.