Question

Two ships leave a dock at the same time. One sails northeast at the rate of 8.5 miles an hour, the other sails north at the rate of 10 miles an hour. How far apart are they at the end of 2 hours?
Anyone can help me using the law of cosine...

Answer 1

@robtobey

Answer 2

@gorv

Answer 3

@phi

Answer 4

First, can you make a sketch of the problem that shows the triangle? and label the parts you know ?

Answer 5

@phi

Answer 6

thats what i know

Answer 7

any idea what the angle is between the two course lines?

Answer 8

is it 45 degrees?

Answer 9

Yes NE is 45º clockwise from N

also, what are the lengths of each course *after two hours* ?

Answer 10

i dont know :D

Answer 11

if it does not display, refresh your browser.
rate of 8.5 miles an hour
that means you move 8.5 miles each hour. Any idea how far you go in 2 hours?

Answer 12

is it the same as 8.5 miles?

Answer 13

it is the same idea as walking. If you walked for one hour and went 1 mile, how far would you walk if you walked for two hours? would it be just 1 mile ?

Answer 14

2 miles

Answer 15

yes. And if you sailed 8.5 miles in 1 hour, how far do you sail in 2 hours ?

Answer 16

17 miles?

Answer 17

yes

Answer 18

so the boat going northeast goes 17 miles

how far does the boat going north go in 2 hours?

Answer 19

i can clearly understand if you draw the figure :D

Answer 20

the other sails north at the rate of 10 miles an hour
how far does it go in 2 hours?

Answer 21

20 miles?

Answer 22

yes.
now draw a line that is 20 long going straight up
and a line going NE (45 degrees) that is 17
You don't have to be exact, but show the first line is a bit longer than the second
label the lengths of each line
label the angle between them

finally, connect the ends of each line to form a triangle.
can you do that ?