解：??$(1)tan A=\frac {a}b=\frac {15}{9}=\frac {5}{3}，$????$tan B=\frac b{a}=\frac {9}{15}=\frac {3}{5}$??
??$(2)$??不妨令??$a=2，$??則??$c=3$??
由勾股定理可得??$b=\sqrt {c^2-a^2}=\sqrt 5$??
∴??$tan A=\frac {a}b=\frac 2{\sqrt 5}=\frac {2\sqrt 5}5，$????$tan B=\frac b{a}=\frac {\sqrt 5}2$??
??$(3)$??不妨令??$b=1，$??則??$c=4$??
由勾股定理可得??$a=\sqrt {c^2-b^2}=\sqrt {15}$??
∴??$tan A=\frac {a}b=\sqrt {15}，$????$tan B=\frac b{a}=\frac 1{\sqrt {15}}=\frac {\sqrt {15}}{15}$?
