Question

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: Identify triangle sides

Sides: home-post (3mi), post-gas (4mi), gas-home (5mi).

Step2: Check right triangle

$3^2 + 4^2 = 9 + 16 = 25 = 5^2$, so right angle at post office.

Step3: Find smallest angle

Smallest angle opposite shortest side (3mi, opposite gas station).

Answer:

A. It is at the gas station.