1. **State the problem:** We have a triangle with two sides of lengths 2 and 17. We want to find the smallest possible whole number length for the third side. 2. **Recall the triangle inequality theorem:** For any triangle with sides $a$, $b$, and $c$, the sum of the lengths of any two sides must be greater than the length of the third side. This gives us three inequalities: $$a + b > c$$ $$a + c > b$$ $$b + c > a$$ 3. **Apply the inequalities to our sides:** Let the third side be $x$. Then: - $2 + 17 > x \implies 19 > x$ - $2 + x > 17 \implies x > 15$ - $17 + x > 2$ (always true since $x$ is positive) 4. **Combine the inequalities:** From above, $x$ must satisfy: $$15 < x < 19$$ 5. **Find the smallest whole number:** The smallest whole number greater than 15 is 16. **Final answer:** The smallest possible whole number length for the third side is $\boxed{16}$.