Question

three friends arrange to meet at a park entrance, but each friend ends up at a different entrance, as shown in the diagram.
pat is at a right angle from chris and jaime, and chris is at a 48° angle from pat and jaime. which statements are true? check all that apply.
□ jaime is at the smallest angle from the two friends.
□ pat is at an angle of 90° to chris and jaime.
□ the path between jaime and chris is the shortest because it is adjacent to the smallest angles.
□ if they meet at pat’s entrance, then chris will have walked a shorter distance than jaime.
□ if they meet at jaime’s entrance, then pat will have walked a longer distance than chris.

Explanation:

Step1: Calculate Jaime's angle

Sum of triangle angles = 180°. Jaime's angle = 180° - 90° - 48° = 42°.

Step2: Evaluate each statement

• Jaime's angle (42°) < Chris's (48°) < Pat's (90°): True.
• Pat's angle is 90°: True.
• Shortest side opposite smallest angle (Jaime-Chris opposite Pat's 90°: longest): False.
• Chris to Pat < Jaime to Pat (shorter side opposite smaller angle): True.
• Pat to Jaime < Chris to Jaime (shorter side opposite smaller angle): False.

Answer:

Jaime is at the smallest angle from the two friends., Pat is at an angle of 90° to Chris and Jaime., If they meet at Pat’s entrance, then Chris will have walked a shorter distance than Jaime.