# Math

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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?

• Math - ,

to get the resultant or the total distance, we use distance formula:
d = sqrt[ (x2-x1)^2 + (y2-y1)^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 x-axis 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/y-axis,
90 - 59.3 = 30.7 degrees from south

thus distance = 37.22 km , 30.7 degrees from south

hope this helps~ :)

• Math - ,

Thank you so much! This definitely helped! =)