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:

Step1: Recall angle - side relationship in a triangle

In a triangle, the side opposite the smaller angle is shorter.

Step2: Compare the angles

We have two angles in the triangle formed by Michael, Jacob and the ship: \(37^{\circ}\) and \(48^{\circ}\). Since \(37^{\circ}<48^{\circ}\), the side opposite the \(37 - degree\) angle is shorter. The angle of \(37^{\circ}\) is the angle between the other dock (Jacob's dock) and the line connecting Jacob and the ship. So the distance from Jacob's dock to the ship is shorter.

Answer:

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