## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 7 - Applications of Trigonometry and Vectors - Section 7.3 The Law of Cosines - 7.3 Exercises - Page 320: 38

#### Answer

$AB + BC \gt AC$ which implies that the shortest distance between points A and C is a straight line.

#### Work Step by Step

Let's consider any triangle ABC. A straight line from point A to point C is along the side AC of the triangle. Suppose that $AB + BC \leq AC$ This statement claims that a path from A to B and then from B to C could be equal to or shorter then the straight line path AC. Then a straight line would not be the shortest distance between points A and C. Clearly this does not make sense. Therefore, it is not possible that $AB + BC \leq AC$. Therefore, $AB + BC \gt AC$ which implies that the shortest distance between points A and C is a straight line.

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