ABCD-rhombus ABCD = 38 degrees AC = 10. Find the height of the rhombus.

Most likely, the condition is about the angle ABC.
The sum of the angles of a rhombus adjacent to one side is 180 °.
Angle С = 180 ° – ∠АВС = 142 °.
We draw the height of the AН to the side of the BC and consider the right-angled triangle AНС.
It knows:
AC = 10 – hypotenuse;
∠ AСН = 1/2 * ∠ С = 71 ° (the diagonal of the rhombus is the bisector).
Let us write in this right-angled triangle the definition of the sine of the angle ACН.
Sin ACH = AH / AC → AH = AC * sin 71 ° = 10 * 0.9455 = 9.455 ≈ 9.5.
We take the sine value in the Bradis table.
Answer: the height of the rhombus is 9.5.