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 nor
theast 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.
1 answer:
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!!!
You might be interested in