1. **Problem statement:** Find the distance between points A and B in the right triangle where the vertical leg is 49 m, the hypotenuse is 35 m, and the other leg is 26 m. 2. **Identify the sides:** In a right triangle, the hypotenuse is the longest side opposite the right angle. Here, the hypotenuse is given as 35 m, but the vertical leg is 49 m, which is longer than 35 m. This is inconsistent with the properties of a right triangle because the hypotenuse must be the longest side. 3. **Check the given data:** Since the hypotenuse cannot be shorter than a leg, the given lengths must be reconsidered. Assuming the hypotenuse is actually 49 m, the vertical leg is 35 m, and the other leg is 26 m, we can proceed. 4. **Use the Pythagorean theorem:** For a right triangle with legs $a$ and $b$, and hypotenuse $c$, the relation is: $$c^2 = a^2 + b^2$$ 5. **Calculate the missing side:** If the hypotenuse $c = 49$ m, and one leg $a = 35$ m, then the other leg $b$ is: $$b = \sqrt{c^2 - a^2} = \sqrt{49^2 - 35^2}$$ 6. **Calculate the squares:** $$49^2 = 2401$$ $$35^2 = 1225$$ 7. **Subtract:** $$2401 - 1225 = 1176$$ 8. **Find the square root:** $$b = \sqrt{1176} = \sqrt{4 \times 294} = 2 \sqrt{294} \approx 2 \times 17.146 = 34.292$$ 9. **Conclusion:** The distance between points A and B, which is the other leg of the triangle, is approximately $34.3$ meters.