Final answer:
By using the Pythagorean theorem, we can calculate the distance between Diana and Florence while considering the bus seating arrangement as a right-angle triangle. The distance between Diana and Neil as one leg, and the distance between Neil and Florence as the hypotenuse, we find the distance between Diana and Florence to be approximately 3.4 feet.
Step-by-step explanation:
To solve the problem related to the positions of Diana, Neil, and Florence on a bus, we can imagine this as a right-angle triangle problem where the distance between Neil and Florence can be considered the hypotenuse of the triangle. Since Diana is directly behind Neil, we can consider the distance between Diana and Neil as one leg of the triangle and the distance between Diana and Florence as the other leg. Using the Pythagorean theorem, we can calculate the missing length (the distance between Diana and Florence).
Given:
Distance between Neil and Diana: 9.3 feet (leg a)
Distance between Neil and Florence: 9.9 feet (hypotenuse c)
We are looking to find the distance between Diana and Florence (leg b).
We can use the Pythagorean theorem:
a2 + b2 = c2
Using the given distances, we solve for b:
- 9.32 + b2 = 9.92
- 86.49 + b2 = 98.01
- b2 = 98.01 - 86.49
- b2 = 11.52
- b = √11.52
- b ≈ 3.4 feet (rounded to the nearest tenth)
Therefore, the distance between Diana and Florence is approximately 3.4 feet.