Good evening Angeline!

Since triangles ABC is similar to triangle STU, we can make the following four conclusions.

1. Angle A = Angle S
2. Angle B = Angle T
3. Angle C = Angle U
4. Corresponding ratios of lengths are equal, that is, AB/ST = AC/SU = BC/TU = number.

Here, angle A corresponds to angle S, so 81 = 81.

Angle B corresponds to angle T, so e is 35.

Angle C corresponds to angle U, so f = 35.

AB/ST = AC/SU = BC/TU

But BC/TU = 4.2/6.3 = 2/3, or TU/BC = 3/2

So the scale factor from triangle ABC to triangle STU is 3/2, or 1.5.

Since the scale factor is 1.5,

ST = 1.5 * AB = 3/2 * 3.8 = 5.7
AC = SU/1.5 = 3.6/1.5 = 2.4

Let me know if you need more explanation.