In triangle ABC, angle C = 90, BC = 1, sinB = 4 / √17. Find AC.

Angle C is 90 degrees, which means triangle ABC is rectangular.
Then the sides BC and AC are the legs of the right-angled triangle ABC.

It is known that sin (B) = 4 / (√17), from here we find the angle B:
angle B = arcsin (4 / (√17)) ≈ arcsin (0.97) ≈ 76 ° (degrees)

The ratio of the opposite leg to the adjacent leg is equal to the tangent of the angle.
AC – leg opposite to corner B.
BC – adjacent to the corner B leg.
So the ratio is correct:
tg (B) = AC / BC
Hence:
AC = BC * tg (B)
AC = 1 * tg (76 °)
AC = 4

Answer: AC = 4.