Answer
5,438,000 miles is the maximum distance that Triton can be from Neptune and still cause a total eclipse.
Work Step by Step
Let $D_N$ be the sun's distance from Neptune and let $D_S$ be the sun's diameter. Let $d_N$ be Triton's distance from Neptune and let $d_T$ be Triton's diameter.
Using similar triangles, we can find the maximum distance that Triton can be from Neptune and still cause a total eclipse:
$\frac{D_S}{D_N} = \frac{d_T}{d_N}$
$d_N = \frac{d_T~D_N}{D_S}$
$d_N = \frac{(1680~mi)(2,800,000,000~mi)}{(865,000~mi)}$
$d_N = 5,438,000~mi$
5,438,000 miles is the maximum distance that Triton can be from Neptune and still cause a total eclipse.
