Question

michael and jacob are standing on two docks that are 20 miles apart. they are watching a ship that is out in the ocean. the angle between the dock and the line connecting michael and the ship is 48°, and the angle between the other dock and the line connecting jacob and the ship is 37°. if the ship can travel to either dock, which dock would be closest? explain your answer. michael 48° 20 mi. jacob ship 37° michael’s dock would be closer because the angle opposite is smaller. jacob’s dock would be closer because the angle opposite is smaller. michael’s dock would be closer because the docks are 20 miles apart. jacob’s dock would be closer because the docks are 20 miles apart.

Explanation:

Step1: Identify triangle sides/angles

The triangle has sides: Michael-Jacob = 20 mi (opposite ship's angle), Michael-ship (opposite 37°), Jacob-ship (opposite 48°).

Step2: Apply triangle side-angle relation

In a triangle, shorter side ↔ smaller opposite angle. 37° < 48°, so side opposite 37° (Michael-ship) is shorter.

Answer:

Michael's dock would be closer because the angle opposite is smaller.