SOLUTION: Describe the resultant as an ordered pair a canoe heading 30 degrees west of north is being paddled at a rate of 7 mi/hr. The current is pushing the canoe 20 degrees south of we

Question 714767: Describe the resultant as an ordered pair
a canoe heading 30 degrees west of north is being paddled at a rate of 7 mi/hr. The current is pushing the canoe 20 degrees south of west at a rate of 3 mi/hr. Find the resulting speed and direction of the canoe.
I dont understand how to set up this problem and have know idea what to do. Please, if you can not graph it, then can you say the steps clearly? Alrighty...
THanks
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Arrow OB, with length , represents the current velocity.
Arrow OA, with length , represents the paddling velocity (relative to the water).
They add up to yield arrow OC, representing the canoe's velocity (relative to the ground).
OA makes an angle of with the positive y-axis,
so the coordinates of A are
and
(rounded values).
OB makes an angle of with the negative x-axis,
so the coordinates of B are
and
(rounded values).
The coordinates represent how far (in miles) the canoe would move in one hour
to the East (for ), and to the North (for )
under the influence of each velocity.
We can represent those velocities (speed and direction)
by those pairs of coordinates.
The resultant speed is represented by the coordinates of point C
and

The coordinates of C are the ordered pair (-6.319, 5.036), which represents the velocity of the canoe with respect to the ground.
From those coordinates we can find
the length of OC, which represents the resultant speed,
and the angle OC makes with the positive y-axis which tells us the direction.

The speed is about 8 mph.
The angle of OC with the the positive y-axis tells us the direction as an angle West of North
-->
The direction is about West of North.
That's the angle the direction forms with the North direction.
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