Answer
The measure of angle A is $44{}^\circ $
Work Step by Step
Here, $a=18.2cm,b=20.5cm$ and $c=26.1cm$
Use the law of cosines to find the measure of angle A as,
${{a}^{2}}={{b}^{2}}+{{c}^{2}}-2bc\text{ }\cos A$ …… (1)
Substitute the values of a, b and c in equation (1),
$\begin{align}
& {{\left( 18.2 \right)}^{2}}={{\left( 20.5 \right)}^{2}}+{{\left( 26.1 \right)}^{2}}-2\left( 20.5 \right)\left( 26.1 \right)\text{ }\cos A \\
& 331.24=416.16+681.21-\left( 1070.1 \right)\text{ }\cos A \\
& 331.24=1097.37-\left( 1070.1 \right)\text{ }\cos A
\end{align}$
Subtract 1097.37 from both sides:
$\begin{align}
& 331.24-1097.37=1097.37-\left( 1070.1 \right)\text{ }\cos A-1097.37 \\
& -766.13=-\left( 1070.1 \right)\text{ }\cos A
\end{align}$
Divide both sides by $-1070.1$ to isolate $\cos A$,
$\begin{align}
& \frac{-766.13}{-1070.1}=\frac{-1070.1}{-1070.1}\text{ }\cos A \\
& 0.7159=\cos A
\end{align}$
Therefore, the value of A is,
$\begin{align}
& A={{\cos }^{-1}}\left( 0.7159 \right) \\
& =44{}^\circ
\end{align}$
Therefore, the measure of angle A is $44{}^\circ $.
