Answer
$A=25.0^{\circ}$
Work Step by Step
The law of sines in the case of this question is:
$\frac{a}{\sin A}=\frac{b}{\sin B}$
We substitute the values of $a,b$ and $A$ in the formula to find $A$:
$\frac{a}{\sin A}=\frac{b}{\sin B}$
$\frac{127}{\sin 129.7}=\frac{69.8}{\sin A}$
$\sin A\times127=69.8\times \sin 129.7$
$\sin A=\frac{69.8\times \sin 129.7}{127}$
We use a calculator to find the value of $\sin 129.7$:
$\sin A=\frac{69.8\times \sin 129.7}{127}$
$\sin A=\frac{69.8\times 0.76940}{127}$
$\sin A=0.422867$
$A=\sin^{-1} 0.422867$
$A=25.02\approx25.0$
Therefore, $A=25.0^{\circ}$.
