Final answer:
The longest side of the trip is from the library to home, indicating that the largest angle is opposite this side at the mall. Therefore, the trip forms a triangle with the largest angle at the mall.
Step-by-step explanation:
The student describes a journey with three distinct legs: 3 miles north, 2 miles west, and then 3.6 miles to return home. These legs form a triangle, and to determine where the largest angle is formed, we should look at the longest side of the triangle, which is usually opposite the largest angle. The trip from the library to home is 3.6 miles, which is longer than both the trip from home to the mall (3 miles) and the trip from the mall to the library (2 miles). Since the longest side is the 3.6 miles back home, the largest angle will be at the point opposite this side, which is where the first two legs of the journey meet, the mall. Therefore, the entire trip forms a triangle, and the largest angle formed during the trip is at the mall.
Reiterating the answer, the entire trip forms a triangle, and option 2 is correct: the largest angle formed during his trip is at the mall.