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. michaels dock would be closer because the angle opposite is smaller. jacobs dock would be closer because the angle opposite is smaller. michaels dock would be closer because the docks are 20 miles apart. jacobs dock would be closer because the docks are 20 miles apart.

Explanation:

In a triangle, the side opposite the smaller angle is shorter. The angle opposite Michael's dock - ship distance is \(37^{\circ}\), and the angle opposite Jacob's dock - ship distance is \(48^{\circ}\). Since \(37^{\circ}<48^{\circ}\), the side (distance) opposite \(37^{\circ}\) (Michael's dock - ship distance) is shorter.

Answer:

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