You use the pythagorean theorem to calculate the missing sides.
formula: a^2+b^2=c^2
a=leg, b=leg, c=hypotenuse.
substitute the lengths in and solve for the missing length.
1. 5^2+12^2=c^2 simplify exponents
25+144=c^2 add
169=c^2 square root both sides
a.13
2. 8^2+b^2=10^2
b.6
3. 15^2+20^2=c^2
b.25
4. Distance formula 5sqrt2
c.7