Answer
The given statement makes sense.
Work Step by Step
The given statement makes complete sense because the exact value for the trigonometric functions of $60{}^\circ \And 45{}^\circ $ can be calculated with the sum formula to calculate $\sin {{105}^{\circ }}$
$\begin{align}
& \sin 105{}^\circ =\sin \left( 60{}^\circ +45{}^\circ \right) \\
& =\sin 60{}^\circ \cos 45{}^\circ +\cos 60{}^\circ \sin 45{}^\circ \\
& =\frac{\sqrt{3}}{2}\cdot \frac{1}{\sqrt{2}}+\frac{1}{2}\cdot \frac{1}{\sqrt{2}}
\end{align}$
Then, further solving the equation, the result will be:
$\begin{align}
& \sin 105{}^\circ =\frac{\sqrt{2}\left( \sqrt{3}+1 \right)}{4} \\
& =\frac{1.4142\left( 1.7320+1 \right)}{4} \\
& =0.9656
\end{align}$
Thus, the given statement makes sense.
