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.

Explanation:

Step1: Recall angle - side relationship in a triangle

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

Step2: Identify the angles

The angle opposite Nigel's distance to the treasure chest is $80^{\circ}$, and the angle opposite Mia's distance to the treasure chest is $65^{\circ}$.

Step3: Compare the angles

Since $65^{\circ}<80^{\circ}$, the side opposite the $65^{\circ}$ angle (Mia's distance to the chest) is shorter.

Answer:

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