Question 1098036
<br>You didn't say the triangle was a right triangle.  However, since you are using {{{a^2+b^2=c^2}}} I will assume it is.<br>
There are of course two possibilities, with two different answers.  The missing side could be the longest side (hypotenuse), with the 5 and 10 being the legs; or the 10 could be the hypotenuse, with the missing side one of the legs.<br>
(1) If the hypotenuse is the missing side, then it is c, and the 5 and 10 are the a and b.  So
{{{5^2+10^2 = c^2}}}
{{{25+100 = c^2}}}
{{{125 = c^2}}}
{{{c = sqrt(125) = 5*sqrt(5)}}}<br>
(2) If 10 is the hypotenuse, then
{{{5^2+b^2 = 10^2}}}
{{{25+b^2 = 100}}}
{{{b^2 = 75}}}
{{{b = sqrt(75) = 5*sqrt(3)}}}