1. **State the problem:** We need to solve for $x$ in a right triangle where the hypotenuse is 80 ft, one leg is 48 ft, and the other leg is split into two segments: 30 ft and $x$ ft. 2. **Identify the right triangle and apply the Pythagorean theorem:** The Pythagorean theorem states that in a right triangle, the square of the hypotenuse ($c$) equals the sum of the squares of the legs ($a$ and $b$): $$c^2 = a^2 + b^2$$ 3. **Assign values:** Let the hypotenuse $c = 80$ ft, one leg $a = 48$ ft, and the other leg $b = 30 + x$ ft. 4. **Write the equation:** $$80^2 = 48^2 + (30 + x)^2$$ 5. **Calculate squares:** $$6400 = 2304 + (30 + x)^2$$ 6. **Isolate the squared term:** $$6400 - 2304 = (30 + x)^2$$ $$4096 = (30 + x)^2$$ 7. **Take the square root of both sides:** $$\sqrt{4096} = \sqrt{(30 + x)^2}$$ $$64 = |30 + x|$$ 8. **Solve for $x$ considering both positive and negative cases:** Case 1: $30 + x = 64$ $$x = 64 - 30 = 34$$ Case 2: $30 + x = -64$ $$x = -64 - 30 = -94$$ 9. **Interpret the solution:** Since $x$ represents a length, it must be positive. Therefore, the valid solution is: $$\boxed{34}$$ ft.