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 the gas station.
it is at lucys home.
it is at the post office.
it depends on the direction lucy is traveling.

Explanation:

Step1: Recall triangle - side relationship

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

Step2: Identify the shortest side

The side - lengths of the triangle are 3 miles, 4 miles, and 5 miles. The shortest side is 3 miles.

Step3: Determine the angle opposite the shortest side

The 3 - mile side is between the post - office and home. So the angle at the gas station is opposite the 3 - mile side.

Answer:

It is at the gas station.