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?

Answer 1

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

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Answer 2

Mia is the one who is closer to the treasure chest. A theorem in Triangle Inequalities state that lines opposite of bigger angles have longer sides. In the case of this triangle, the angle opposite of Mia’s path is smaller than the angle opposite of Nigel’s. To confirm the actual distance, the law of sine and law of cosine can be used.