Final answer:
To determine the total distance flown by the bird, we use the Pythagorean theorem to calculate the hypotenuse of the right triangle formed by the library, courthouse, and swimming pool. The total distance comes to 14.3 miles.
Step-by-step explanation:
To find the total distance flown by the bird, we first calculate each segment of the trip and then sum them up. The bird flies directly from the courthouse to the library which is 2 miles south. Next, it flies from the library to the community swimming pool which is 6 miles east. Finally, the bird returns to the courthouse by flying directly from the swimming pool. This path forms a right triangle, with the legs being the distance between the library and the courthouse, and the library and the swimming pool. The hypotenuse of this triangle is the direct distance between the courthouse and the swimming pool.
Using the Pythagorean theorem (a² + b² = c²) where a is 2 miles, and b is 6 miles, we can find the hypotenuse c:
- a² = 2² = 4
- b² = 6² = 36
- c² = 4 + 36 = 40
- c = √40 ≈ 6.3 miles
The total distance flown by the bird is the sum of all three segments:
- 2 miles (courthouse to library)
- 6 miles (library to swimming pool)
- 6.3 miles (swimming pool to courthouse)
Total distance = 2 + 6 + 6.3 = 14.3 miles
Therefore, if the bird followed this path, it would fly a total distance of 14.3 miles.