Question

Suppose a boat travels due north for 17 miles, then heads northeast for 8 miles. How far from the original starting position is the boat?

I know this deals with law of Cosines, but I'm very confused.

I tried the distance formula, but I got 26 which I know is wrong as it can't be more than the other two sides added together which would be 25.

Answer 1

I got 689^.5

Answer 2

You calculation for 25 doesnt take into account the new triangle formed, you just added up a straight line and a line at a 25 degree angle

Answer 3

make sense?

Answer 4

45 not 25

Answer 5

Now I'm really confused actually ._.

Answer 6

How is it possibly 45 miles away?

Answer 7

You calculation for 25 doesnt take into account the new triangle formed, you just added up a straight line and a line at a 45 degree angle

Answer 8

Well, 25 is the whole distance traveled.

So if I were to make a straight line from that it couldn't possibly be more than 25

Answer 9

Sorry, think I messed up earlier on the problem

Answer 10

Oh >.<

What did I do wrong?

Answer 11

http://mathworld.wolfram.com/LawofCosines.html

Using the first formula you should be able to see the triangle match up pretty easily

Answer 12

Wait isn't it 17 and then 8? not 7 then 17?

Answer 13

c=17, b=8

Answer 14

Maybe I shouldnt do trig problems D:

Answer 15

I think you're confusing me more xD

Answer 16

Sorry

Answer 17

Does the drawing make sense?

Answer 18

\[a^2 = b^2+c^2-2*b* c *cosA\]

Answer 19

you want "a" for the distance travelled

Answer 20

I mean, that doesn't help me solve what A side is

I know it's more than 18 and less than 25...

Answer 21

you need to solve little a with that equation, law of cosines

Answer 22

understand?

Answer 23

\[a^{2} \]=64+289-2(8)(17)(90)

Is this correct?

Answer 24

or is it

\[a ^{2}\]135=64+289-2(8)(17)(135)