Question

applying theorems to real - world scenarios
lucy has to run two errands. she starts from home and travels 3 miles
south to the post office. from the post office, she travels 4 miles east to
the gas station. then, from the gas station, she travels 5 miles to return
home. the entire trip forms a triangle.
what was the smallest angle made in her trip?
it is at lucys home.
it is at the gas station.
it is at the post office.
it depends on the direction lucy is traveling.

Explanation:

Step1: Recall the triangle side - angle relationship

In a triangle, the smallest angle is opposite the shortest side.

Step2: Identify the sides of the triangle

The sides of the triangle are \(a = 3\) (home - post office), \(b=4\) (post office - gas station), \(c = 5\) (gas station - home). The shortest side is \(a = 3\).

Step3: Determine the angle opposite the shortest side

The angle opposite the side of length \(3\) (home - post office side) is at the gas station.

Answer:

It is at the gas station.