In order to calculate the value of 'a', we can use the Pythagorean theorem, where the hypotenuse squared is equal the sum of each leg squared:
[tex]h^2=l^2_1+l^2_2[/tex]
In this case, the hypotenuse is 10 and the legs are 'a' and 7, so we have:
[tex]\begin{gathered} 10^2=a^2+7^2 \\ 100=a^2+49 \\ a^2=100-49 \\ a^2=51 \\ a=\sqrt[]{51} \end{gathered}[/tex]
So the value of 'a' is √51.
