Use the Pythagorean Theorem to relate the lengths of the legs of the right triangle on the picture to the length of the hypotenuse:
[tex]40^2+a^2=50^2[/tex]
Solve for a:
[tex]\begin{gathered} \Rightarrow1600+a^2=2500 \\ \Rightarrow a^2=2500-1600 \\ \Rightarrow a^2=900 \\ \Rightarrow a=\sqrt[]{900} \\ \Rightarrow a=30 \end{gathered}[/tex]
Therefore, the value of a is:
[tex]30[/tex]
