1. **State the problem:** We have a right triangle with a hypotenuse of 78 ft and one leg of 72 ft. We need to find the length of the missing leg $a$. 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse, and $a$, $b$ are the legs. 3. **Apply the formula:** Here, $c = 78$ ft, $b = 72$ ft, and $a$ is unknown. $$a^2 + 72^2 = 78^2$$ 4. **Calculate squares:** $$a^2 + 5184 = 6084$$ 5. **Isolate $a^2$:** $$a^2 = 6084 - 5184$$ $$a^2 = 900$$ 6. **Find $a$ by taking the square root:** $$a = \sqrt{900}$$ $$a = 30$$ 7. **Answer:** The length of the missing leg $a$ is 30 feet.