ad a).
(|BC|)^2+(|AC|)^2=(|AB|)^2
7^2+24^2=(|AB|)^2
49+576=(|AB|)^2
(|AB|)^2=625
|AB|=25
ad b).
(|AC|)^2+(|BC|)^2=(|AB|)^2
(|AC|)^2+(13\frac{1}{3})^2=(13\frac{2}{3})^2
(|AC|)^2=(\frac{41}{3})^2-(\frac{40}{3})^2
(|AC|)^2=(\frac{1681}{9})^2-(\frac{1600}{9})^2
(|AC|)^2=\frac{81}{9}
(|AC|)^2=9
|AC|=3
ad c).
(|BC|)^2+(|AC|)^2=(|AB|)^2
(|BC|)^2+(\sqrt{2})^2=(\sqrt{3})^2
(|BC|)^2+2=3
(|BC|)^2=1
|BC|=1