1. Among the triangles with side lengths being consecutive natural numbers and a perimeter not exceeding 100, the number of acute triangles is $\qquad$ .
1. 29

Solution Let the three sides of the triangle that satisfies the condition be
$$
n-1, n, n+1 \text{, }
$$

then $\left\{\begin{array}{l}(n-1)+n+(n+1) \leqslant 100, \\ (n-1)+n>n+1 .\end{array}\right.$
which is $\left\{\begin{array}{l}n \leqslant 33, \\ n>2 .\end{array}\right.$
Therefore, $n=3,4, \cdots, 33$.
When $n=3$, $2^{2}+3^{2}>0$, the triangle is an acute triangle.
Thus, the number of acute triangles that satisfy the condition is 29.