1. The three sides of an obtuse triangle are $m, m+1, m+2$, then the range of the real number $m$ is $\qquad$
$$
\left\{\begin{array} { l } 
{ m + m + 1 > m + 2 , } \\
{ m ^ { 2 } + ( m + 1 ) ^ { 2 } > 1, \\
m^{2}-2 m-3<0
\end{array} \Rightarrow 1<m<3\right.\right. \text {. }
$$

Therefore, the range of real number $m$ is $(1,3)$.