1. **State the problem:** We have a right triangle with vertices M, C, and D, right angle at C. Point B lies on segment CD, and we want to find the length of BC. 2. **Given data:** - MC = 18.3 m - MD = 24 m - AB = 5.2 m (vertical segment on CD with A above B) 3. **Understand the setup:** Since the right angle is at C, triangle MCD is right-angled at C. 4. **Find CD:** Using the Pythagorean theorem in triangle MCD, $$CD = \sqrt{MD^2 - MC^2} = \sqrt{24^2 - 18.3^2}$$ Calculate: $$24^2 = 576$$ $$18.3^2 = 334.89$$ $$CD = \sqrt{576 - 334.89} = \sqrt{241.11} \approx 15.53\text{ m}$$ 5. **Locate B on CD:** Since AB = 5.2 m and A is above B on CD, and CD is vertical, the length BC is the difference between CD and AB: $$BC = CD - AB = 15.53 - 5.2 = 10.33\text{ m}$$ **Final answer:** $$\boxed{BC \approx 10.33\text{ meters}}$$