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 pats entrance, then chris will have walked a shorter distance than jaime. if they meet at jaimes entrance, then pat will have walked a longer distance than chris.

Explanation:

Step1: Analyze given angles

We know Pat - Chris - Jaime form a right - triangle with $\angle$Pat = 90° and $\angle$Chris=48°. Then $\angle$Jaime = 180°-(90° + 48°)=42°.

Step2: Evaluate each statement

• For the statement "Jaime is at the smallest angle from the two friends": Since $\angle$Jaime = 42°,$\angle$Chris = 48° and $\angle$Pat=90°, Jaime has the smallest angle among them, so this statement is true.
• For the statement "Pat is at an angle of 90° to Chris and Jaime": Given in the problem, this is true.
• For the statement "The path between Jaime and Chris is the shortest because it is adjacent to the smallest angles": In a right - triangle, the hypotenuse (path between Jaime and Chris) is the longest side, so this statement is false.
• For the statement "If they meet at Pat’s entrance, then Chris will have walked a shorter distance than Jaime": In a right - triangle, the side opposite the smaller non - right angle is shorter. Since $\angle$Chris = 48° and $\angle$Jaime = 42°, the side opposite $\angle$Chris is shorter than the side opposite $\angle$Jaime when going to Pat's entrance, so this statement is true.
• For the statement "If they meet at Jaime’s entrance, then Pat will have walked a longer distance than Chris": The side opposite $\angle$Pat is longer than the side opposite $\angle$Chris when going to Jaime's entrance, so this statement is true.

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.
If they meet at Jaime’s entrance, then Pat will have walked a longer distance than Chris.