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. 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 principle that the largest angle is opposite the longest side. The sides of the triangle are: from home to mall (\(3\) miles), mall to library (\(2\) miles), and library to home (\(3.6\) miles). The longest side is \(3.6\) miles (library to home), so the angle opposite to it is at the mall (between home - mall - library). Let's verify:

• Side home - mall: \(3\) miles.
• Side mall - library: \(2\) miles.
• Side library - home: \(3.6\) miles (longest).

The angle opposite the longest side (library - home) is the angle at the mall (between home, mall, and library).

Answer:

at the mall