SOLUTION: A family is traveling due west on a road that passess a famous landmark. At a given time the bearing to the landmark is N 62 W and after the family travels 5 miles farther the bea

Question 61155This question is from textbook
: A family is traveling due west on a road that passess a famous landmark. At a given time the bearing to the landmark is N 62 W and after the family travels 5 miles farther the bearing is N 38 W. What is the closest the family will come to the landmark while on the road?
Question: I came up with obtuse triangle with angles of 28, 128, 24. Found length of the side to be 5.77.by using law of sines. the answer in the book is 4.55. What did I do wrong? This question is from textbook

Answer by 303795(602) (Show Source): You can put this solution on YOUR website!
Nothing wrong so far. The car is still travelling along the road however so it will get closer to the landmark.
As you obviously know what you are doing I will only give you a general idea rather than solve it all for you.
Use the diagram you already have to find how far the car was when it started travelling from the landmark (9.68 miles).
The car will be closest when the landmark is due north. Draw a new diagram using the starting position of the car (which is 9.68 from the landmark) to get a right angle triangle. This will result in the answer of 4.55 miles.
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