1. **State the problem:** The Sears Tower's total height including the antenna is 1729 feet. The difference in height between the building and the antenna is 1171 feet. We need to find the height of just the building part. 2. **List the information:** - Total height (building + antenna): $1729$ feet - Difference in height (building - antenna): $1171$ feet 3. **Write two equations:** Let $B$ = height of the building, $A$ = height of the antenna. $$B + A = 1729$$ $$B - A = 1171$$ 4. **Solve the system:** Add the two equations: $$ (B + A) + (B - A) = 1729 + 1171 $$ $$ 2B = 2900 $$ $$ B = \frac{2900}{2} = 1450 $$ 5. **Find the antenna height:** Substitute $B=1450$ into $B + A = 1729$: $$ 1450 + A = 1729 $$ $$ A = 1729 - 1450 = 279 $$ **Answer:** The building part of the Sears Tower is $1450$ feet tall.