1. **Problem statement:** We have a crane with a vertical tower 22 m tall and a horizontal arm 44 m long. A support cable forms a right triangle with vertical segment 24 m and horizontal segment $l$ m, and a small tower of height $h$ m above the crane arm. We need to find $h$ and the total length of the support cable. 2. **Understanding the setup:** The vertical tower is 22 m, and the small tower rises $h$ m above the crane arm, so the total vertical height of the cable is $22 + h$ m. 3. **Using the Pythagorean theorem:** The cable forms the hypotenuse of a right triangle with vertical side $22 + h$ and horizontal side 44 m. 4. **Given vertical segment of cable is 24 m:** This means the vertical part of the cable above the crane arm is $h = 24 - 22 = 2$ m. 5. **Calculate the total length of the cable $l$:** Using Pythagoras, $$l = \sqrt{(22 + h)^2 + 44^2} = \sqrt{(22 + 2)^2 + 44^2} = \sqrt{24^2 + 44^2}$$ 6. **Calculate:** $$24^2 = 576$$ $$44^2 = 1936$$ $$l = \sqrt{576 + 1936} = \sqrt{2512} \approx 50.12$$ 7. **Final answers:** - Height $h = 2.00$ m - Cable length $l \approx 50.12$ m