1. Problem: Mary hiked 9 km north and 12 km east. How far was she from her starting point? 2. This is a right triangle problem where the legs are 9 km and 12 km, and we want to find the hypotenuse $k$. 3. Use the Pythagorean theorem: $$k = \sqrt{9^2 + 12^2}$$ 4. Calculate the squares: $$9^2 = 81, \quad 12^2 = 144$$ 5. Sum the squares: $$81 + 144 = 225$$ 6. Take the square root: $$k = \sqrt{225} = 15$$ 7. So, Mary is 15 km from her starting point. --- Note: The second problem about the ladder is not solved as per instructions to solve only the first problem.