SOLUTION: Solve the following problem. Draw a diagram and show your work. A ship travels a distance of 82 miles in the direction N 18degrees E and then travels 46 miles in the direction S

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Question 329518: Solve the following problem. Draw a diagram and show your work.
A ship travels a distance of 82 miles in the direction N 18degrees E and then travels 46 miles in the direction S 72degrees E. Find the distance and bearing of the ship's final position from its original position.
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
When the ship goes 18 degrees and then turns to a bearing of S72E, it turns 90 degrees. 72+18=90.
Another way to look at it, S72E is equal to an azimuth of 108 degrees and a bearing of N18E is equal to an azimuth of 18 degrees. 108-18=90.
So, we have a right triangle to deal with.
By Pythagoras, the distance back to the origin is sqrt%2882%5E2%2B46%5E2%29=2%2Asqrt%282210%29=94.02 miles.
We can find the bearing from the origin to the ship by
18%2Barctan%2846%2F82%29=47.29 degrees.
A bearing of N47.3E