Vector Application problem

[Rickey Smiley]

A boat leaves the marina and sails 14 miles west, then 10 miles northwest. How far, in miles, from the marina is the boat? (Round your answer to the nearest hundredth if necessary.)

 

[Deleted member 4993]

A boat leaves the marina and sails 14 miles west, then 10 miles northwest. How far, in miles, from the marina is the boat? (Round your answer to the nearest hundredth if necessary.)

If I were to do your assignment,

I would make a sketch of the position vector of the boat, w.r.t. the marina, and calculate its magnitude.​

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem

 

[HallsofIvy]

"Northwest" is 45 degrees above "west" so the second leg makes a 180- 45= 135 degrees with the first leg. What is the length of the third side of a triangle with two legs of length 14 miles and 10 miles with angle 135 degrees between them?

(Cosine law!)