A boy tried to align 480 cans in the shape of a triangle with one can in the $1^{\text{st}}$ row, 2 cans in the $2^{\text{nd}}$ row, and so on. In the end, 15 cans were left over. How many rows does this triangle have?
Suppose the triangle is composed of $n$ rows, so $1+2+3+\cdots+n$ cans were used, thus

$$
480-15=1+2+\cdots+n=\frac{n(n+1)}{2} \Longrightarrow n^{2}+n-930=0
$$

Solving the equation $n^{2}+n-930=0$, we get:

$$
n=\frac{-1 \pm \sqrt{1+4 \times 930}}{2}=\frac{-1 \pm 61}{2}
$$

Thus, $n=30$ is the only positive solution to this equation. Therefore, the triangle has 30 rows.