Question

nigel and mia are searching for a treasure chest under water. the straight line distance between them is 100 meters. given the angles in the diagram, who is closer to the treasure chest and why? nigel is closer because his distance to the chest is opposite the larger angle. mia is closer because her distance to the chest is opposite the smaller angle. nigel is closer because his distance from the chest is 100 meters. mia is closer because her distance from the chest is 100 meters.

Explanation:

In a triangle, the side opposite the smaller angle is shorter. The sum of angles in a triangle is \(180^{\circ}\). So the third angle (opposite the side between Nigel and Mia, which is 100 m) is \(180-(65 + 80)=35^{\circ}\). Nigel's distance to the chest is opposite the \(80^{\circ}\) angle, and Mia's distance is opposite the \(65^{\circ}\) angle. Since \(65^{\circ}<80^{\circ}\), the side opposite \(65^{\circ}\) (Mia's distance) is shorter.

Answer:

Mia is closer because her distance to the chest is opposite the smaller angle.