Math
posted by Lisa on .
A boat in calm seas travels 19 km east and 32 km south. Find the distance and direction of the trip, relative to the south. What is the distance? What is the direction?
I'm confused about how to solve this problem. Could someone show me the steps?

to get the resultant or the total distance, we use distance formula:
d = sqrt[ (x2x1)^2 + (y2y1)^2 ]
where
(x1,y1) is our reference/starting point, and
(x2,y2) is the final point
assuming our reference point is at the origin which is at (0,0)
d = sqrt[ (x2)^2 + (y2)^2 ]
substituting:
d = sqrt[ (19)^2 + (32)^2 ]
d = 37.22 km
*note: we use 32 since it is travelling south/downward direction
getting the direction: let theta = angle from xaxis measured counterclockwise,,
tan (theta) = y/x
tan (theta) = (32)/19
theta = 59.3 degrees
*note: the negative sign means opposite direction, or it is rotated clockwise
since we need the angle to be relative to south/yaxis,
90  59.3 = 30.7 degrees from south
thus distance = 37.22 km , 30.7 degrees from south
hope this helps~ :) 
Thank you so much! This definitely helped! =)