Final answer:
Eva's last leg of the ride, back to the starting point, can be calculated using the Pythagorean theorem, assuming a right angle turn. By squaring the distances of the two legs and taking the square root of their sum, we determine that the last leg of her journey is approximately 6.7 miles.
Step-by-step explanation:
The student's question regards the distance Eva rode on the last leg of her trip back to the starting point after initially bicycling 3 miles north and then 6 miles in another direction. To calculate the distance for the last leg of her trip, we can use the Pythagorean theorem, which applies to right-angled triangles.
Assuming Eva's second leg of the journey was at a right angle to the first leg, we can consider the first 3 miles as one side of the triangle (north direction) and the next 6 miles as the perpendicular side of the triangle (in an east or west direction).
Let's calculate the hypotenuse, which is the last leg of the ride back to the starting point:
- The square of the hypotenuse (last leg) is equal to the sum of the squares of the other two sides.
- So, hypotenuse2 = (3 miles)2 + (6 miles)2.
- Hypotenuse2 = 9 + 36 = 45.
- Therefore, the hypotenuse (last leg) = √45.
After calculating this, we find that the hypotenuse is approximately 6.7 miles.
Therefore, the last leg of Eva's ride is roughly 6.7 miles to the nearest tenth of a mile.