1. **Problem statement:** Calculate the length $d$ of the cable, which is the hypotenuse $AD$ of the right triangle $ABCD$ with sides $AB=45$ m, $BC=9$ m, and $DC=28$ m. 2. **Understanding the problem:** The triangle is right-angled, and $d$ is the hypotenuse. We need to find $d$ using the Pythagorean theorem. 3. **Formula:** For a right triangle with legs $a$ and $b$ and hypotenuse $c$, the Pythagorean theorem states: $$c^2 = a^2 + b^2$$ 4. **Identify the legs:** Here, the legs are $AB + BC$ and $DC$ because points $A$, $B$, $C$, and $D$ form the triangle with $AD$ as hypotenuse. Calculate the length of one leg: $$AB + BC = 45 + 9 = 54\text{ m}$$ The other leg is: $$DC = 28\text{ m}$$ 5. **Apply the Pythagorean theorem:** $$d^2 = (54)^2 + (28)^2$$ $$d^2 = 2916 + 784$$ $$d^2 = 3700$$ 6. **Calculate $d$:** $$d = \sqrt{3700}$$ $$d \approx 60.83\text{ m}$$ 7. **Answer:** The length of the cable $d$ is approximately $60.83$ meters.