From the figure the length of the hypotenuse is

We want hypotenuse$PR$.

We know that $\overline{)R}$ and adjacent side of $\overline{)R}$.

So, we take cosine ratio (or) secant ratio.

i.e., $Cos24°=\frac{adjacentsideto24°}{hypotenuse}$

$\Rightarrow$$Cos24°=\frac{QR}{PR}$

$\Rightarrow$$\cos 24°=\frac{8}{PR}$

$\therefore$$PR=\frac{8}{\cos 24°}$

(or)

$PR=8\times \sec 24°$

$\frac{8}{\cos 24°}$ Is correct.

$8\sec 24°=8\times \frac{1}{\cos 24°}$                    $\left(\therefore \sec \theta =\frac{1}{\cos \theta }\right)$

$=\frac{8}{\cos 24°}$

$\frac{8}{\sin 24°}\ne \frac{8}{\cos 24°}$

$8\cos ec24°\ne \frac{8}{\cos 24°}$