Question

Given the angles in the diagram, who is closer to the treasure chest and why

Answer 1

Please see attached file for my answer.

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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.