Answer
The simplified value of $ a $ is $8$ and the value of $ b $ is $6$.
Work Step by Step
By using the Pythagoras identity in both triangles, we get
$\begin{align}
& {{a}^{2}}+{{b}^{2}}={{10}^{2}} \\
& {{a}^{2}}+{{\left( b+9 \right)}^{2}}={{17}^{2}} \\
\end{align}$
Solve both of the above equations as shown below:
${{a}^{2}}+{{b}^{2}}=100$ (I)
And
$\begin{align}
& {{a}^{2}}+{{\left( b+9 \right)}^{2}}={{17}^{2}} \\
& {{a}^{2}}+{{b}^{2}}+81+18b=289
\end{align}$
Now, put the value of equation (I) and simplify this as shown below:
$\begin{align}
& 100+81+18b=289 \\
& 18b=108 \\
& b=6
\end{align}$
Put the value of $ b $ in equation (I) to get the value of $ a $ as shown below:
$\begin{align}
& {{a}^{2}}+{{6}^{2}}=100 \\
& {{a}^{2}}+36=100 \\
& {{a}^{2}}=64 \\
& a=8
\end{align}$
Hence, the value of $ a $ is 8 and the value of $ b $ is 6.
