Answer
The value of $a$ is $45.20$.
Work Step by Step
Solve the provided expression for a,
$\begin{align}
& \frac{a}{\sin 46\text{ }\!\!{}^\circ\!\!\text{ }}=\frac{56}{\sin 63\text{ }\!\!{}^\circ\!\!\text{ }} \\
& a=\frac{56\times \sin 46\text{ }\!\!{}^\circ\!\!\text{ }}{\sin 63\text{ }\!\!{}^\circ\!\!\text{ }}
\end{align}$
Then, calculate the value of $\sin 46\text{ }\!\!{}^\circ\!\!\text{ }$ and $\sin 63\text{ }\!\!{}^\circ\!\!\text{ }$ on the calculator as:
$\sin 46\text{ }\!\!{}^\circ\!\!\text{ }=0.7193398$ and $\sin 63\text{ }\!\!{}^\circ\!\!\text{ }=0.891006524$
Now, use these values in the above expression,
$\begin{align}
& a=\frac{56\times 0.7193398}{0.891006524} \\
& =\frac{40.2830288}{0.891006524} \\
& =45.2107
\end{align}$
And round off to the nearest decimal.
$a=45.20$.
Thus, the value of $a$ is $45.20$.
