The angle Bragg path is a checked geometry ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The ray triangle pins the sine factor
The rendered ray uses a three-four-five triangle, so the sine factor is 3/5.
sinθ=53
Path difference equals one wavelength
With spacing 5 m, the extra path is 6 m. Order one therefore uses wavelength 6 m.