Final answer:
The distance from the ground to the top of James's ladder can be found using the Pythagorean theorem. The ladder forms a right-angled triangle with the ground and the building, with the ladder as the hypotenuse (10 meters) and the base (5 meters from the building). The correct answer is approximately 8 meters, which is option b).
Step-by-step explanation:
James has positioned a ladder in such a way that it forms a right-angled triangle with the building and the ground. To find the distance from the ground to the top of the ladder, we will use the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this problem, the ladder itself is the hypotenuse of length 10 meters, and the base is 5 meters away from the building.
Let's represent the distance from the ground to the top of the ladder as d. This distance is the other side of the right-angled triangle we're trying to find. According to the Pythagorean theorem:
d² + 5² = 10²
d² + 25 = 100
d² = 100 - 25
d² = 75
d = √75
d = 8.66 meters (approximately)
Therefore, the correct answer is b) 8 meters, which is the distance from the ground to the top of the ladder when rounded to the nearest whole number.