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? mia is closer because her distance to the chest is opposite the smaller angle. mia is closer because her distance from the chest is 100 meters. nigel is closer because his distance from the chest is 100 meters. nigel is closer because his distance to the chest is opposite the larger angle.

Explanation:

Step1: Find the third angle of the triangle

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle be \(x\). Then \(x = 180-(65 + 80)=35^{\circ}\).

Step2: Apply the triangle - side relationship (larger angle - larger side)

In a triangle, the side opposite a larger angle is longer. The side opposite \(35^{\circ}\) (Mia's distance to the chest) is shorter than the side opposite \(65^{\circ}\) (Nigel's distance to the chest).

Answer:

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