Final answer:
The correct distance the ramp extends along the ground from the train, found using the Pythagorean theorem, is approximately 28.28 cm, but this is not an option provided. There seems to be an error in the provided values or available answer choices.
Step-by-step explanation:
To find out how far out from the train the ramp extends along the ground, we need to use the Pythagorean theorem because we are dealing with a right-angled triangle. The vertical height of the triangle is 10 cm (height above the ground when the ramp is extended), and the hypotenuse (the ramp itself) is 30 cm. To find the base of the triangle (the distance from the train on the ground), we calculate it using the formula:
b = √(hypotenuse² - height²) = √(30² - 10²) = √(900 - 100) = √800 ≈ 28.28 cm.
However, none of the provided options exactly match this result. The closest option to our calculated distance would likely be option c) 28.28 cm rounded to the nearest given option, which would be 22.36 cm. There appears to be a mistake either in the question's values or the provided multiple-choice answers.