Well the normal way to go about solving sides of right triangles is by the Pythagorean Theorem:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
where a and b are the two smaller sides and c is always the hypotenuse.
So if we make b = 15 in, c = 20 in, a = ??
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {a}^{2} = {c}^{2} - {b}^{2} \\ \sqrt{ {a}^{2}} = \sqrt{( {c}^{2} - {b}^{2}) } \\ a = \sqrt{( {c}^{2} - {b}^{2}) } [/tex]
Now plug-in for b and c:
[tex]a = \sqrt{( {c}^{2} - {b}^{2}) } \\ a = \sqrt{( {20}^{2} - {15}^{2}) } \\ a = \sqrt{(400 - 225) } = \sqrt{175} \\ a = \sqrt{25} \times \sqrt{7} = 5 \sqrt{7} \: in[/tex]
