Final answer:
To determine the size of the ladder needed, subtract the student's height from the light bulb's height and use the Pythagorean theorem to find the ladder's length.
Step-by-step explanation:
To determine the size of the ladder needed, we need to first calculate the distance between the student and the light bulb. We can subtract the height of the student (6 feet) from the height of the light bulb (12 feet) to find the vertical distance between them. In this case, the vertical distance is 6 feet.
Next, we can use the Pythagorean theorem to find the length of the ladder needed. The ladder, the distance from the student to the base of the ladder, and the distance from the bulb to the base of the ladder form a right triangle. Using the Pythagorean theorem, we can say that the square of the ladder's length is equal to the sum of the squares of the vertical distance and the base distance. Plugging in the values, we have ladder length^2 = 6^2 + 12^2 = 36 + 144 = 180. Taking the square root of 180 gives us the length of the ladder, which is approximately 13.416 feet.
Therefore, the ladder needed is approximately 13.416 feet. None of the given options (a) 9 feet, b) 10 feet, c) 15 feet, d) 18 feet) are correct.