1. **State the problem:** We need to find the range of possible lengths for the third side $n$ of a triangle when the other two sides measure 6 ft and 19 ft. 2. **Recall the triangle inequality theorem:** For any triangle with sides $a$, $b$, and $c$, the length of any side must be less than the sum of the other two sides and greater than their difference. This gives us two inequalities for the third side $n$: $$|a - b| < n < a + b$$ 3. **Apply the theorem:** Here, $a = 6$ and $b = 19$, so: $$|6 - 19| < n < 6 + 19$$ 4. **Calculate the values:** $$|6 - 19| = | -13 | = 13$$ $$6 + 19 = 25$$ 5. **Write the range:** $$13 < n < 25$$ 6. **Interpretation:** The third side must be greater than 13 ft and less than 25 ft to form a valid triangle with sides 6 ft and 19 ft.