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Convenience Stores A and B are 50 miles apart on a stretch of Hwy 12 which runs north/south. Convenience Store C is 14 miles northeast of Convenience Store B. There is a direct route from Convenience Store A to Convenience Store C. What do you know about the distance between stores A and C? Justify your answer.

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Answer:

The distance from A to C along a direct route is either 48 miles or 60.71 miles depending on the interpretation of the question.

Step-by-step explanation:

The two possible interpretations of this question are presented in the attached image to this solution.

From the first interpretation, the three sides can just be related using pythagoras theorem.

AB² = AC² + BC²

AB = 50 miles

AC = ?

BC = 14 miles

50² = AC² + 14²

AC² = 50² - 14² = 2304

AC = 48 miles.

Using the second interpretation, we can relate the 3 sides using cosine rule.

AC² = AB² + BC² - (2)(AB)(BC) cos 135°

AB = 50 miles

AC = ?

BC = 14 miles

AC² = 50² + 14² - (2)(50)(14) cos 135°

AC² = 3685.95

AC = 60.71 miles

Hope this Helps!!!

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