In triangle ABC, a is the length of the side opposite to angle A (side BC), b is the length of the side opposite to angle B (side AC), and c is the length of the side opposite to angle C (side AB)
We can use the cosine rule to find the length of each side
[tex]\begin{gathered} a=\sqrt[]{b^2+c^2-2bc\cos A} \\ b=\sqrt[]{a^2+c^2-2ac\cos B} \\ c=\sqrt[]{a^2+b^2-2ab\cos C} \end{gathered}[/tex]
From the given figure we can see triangle ABC, where We will use the cosine rule to find c
[tex]c=\sqrt[]{a^2+b^2-2ab\cos 90^{\circ}}[/tex]
Since cos(90) = 0, then
[tex]\begin{gathered} c=\sqrt[]{a^2+b^2-2ab(0)} \\ c=\sqrt[]{a^2+b^2-0} \\ c=\sqrt[]{a^2+b^2} \end{gathered}[/tex]
The expression equivalent to c is
[tex]\sqrt[]{a^2+b^2}[/tex]
