Answer
$\frac{\sqrt {55}}{8}$
Work Step by Step
Step 1. Let $u=cos^{-1}\frac{3}{8}$, we have$ cos(u)=\frac{3}{8}$ The range of inverse cosine is $[0,\pi]$, thus
$0\lt u\lt \frac{\pi}{2}$
Step 2. With the results above and use the Pythagorean Identity $sin^2u=1-cos^2u=1-\frac{9}{64}=\frac{55}{64}$
Step 3. $sin(cos^{-1}\frac{3}{8})=sin(u)=\frac{\sqrt {55}}{8}$
