Question

gene starts from home and travels 3 miles north to the shopping mall. from the shopping mall, he travels 2 miles west to the library. then, from the library, he travels about 3.6 miles to return home. the entire trip forms a triangle. library mall home the largest angle formed during his trip is ______ at his home at the mall between the mall and the library between his home and the library

Explanation:

To determine the largest angle in a triangle, we use the relationship between the length of a side and the size of its opposite angle (longer side opposite larger angle).

Step 1: Identify the side lengths of the triangle

• Home to Mall: \( a = 3 \) miles (opposite the angle at the Library)
• Mall to Library: \( b = 2 \) miles (opposite the angle at Home)
• Library to Home: \( c = 3.6 \) miles (opposite the angle at the Mall)

Step 2: Compare the side lengths

We compare the lengths: \( 3.6 > 3 > 2 \). The longest side is \( c = 3.6 \) miles, which is opposite the angle at the Mall.

Step 3: Apply the side - angle relationship

In a triangle, the largest angle is opposite the longest side. Since the longest side (\( 3.6 \) miles) is opposite the angle at the Mall, the largest angle is at the Mall.

Answer:

at the mall