1. **State the problem:** We are given two triangles HFG and KJI with the same angles 88°, 54°, and 38°. We know sides GH = 79, HF = 60 in triangle HFG, and side KI = 42 in triangle KJI. We need to find the length of JK. 2. **Identify the type of problem:** Since the triangles have the same angles, they are similar triangles. Corresponding sides are proportional. 3. **Set up the proportion:** Corresponding sides in similar triangles satisfy: $$\frac{GH}{KI} = \frac{HF}{JK}$$ 4. **Plug in known values:** $$\frac{79}{42} = \frac{60}{JK}$$ 5. **Solve for JK:** Cross multiply: $$79 \times JK = 42 \times 60$$ $$79 \times JK = 2520$$ Divide both sides by 79: $$JK = \frac{2520}{79}$$ Show cancellation: $$JK = \frac{2520}{\cancel{79}}$$ Calculate: $$JK \approx 31.9$$ 6. **Final answer:** The length of JK is approximately **31.9** units.