Answer: Hello mate!
lets define the north as the y-axis and east as the x-axis.
Using the notation (x,y) we can define the initial position of the car as (0,0)
then the car travells 13 mi east, so now the position is (13,0)
then the car travels Y miles to the north, so the position now is (13, Y)
and we know that the final position is 25° degrees north of east of the initial position. This angle says that the distance traveled to the north is less than 13 mi because this angle is closer to the x-axis (or east in this case).
This angle is measured from east to north, then the adjacent cathetus is on the x-axis, in this case, 13mi
And we want to find the distance Y, so we can use the tangent:
Tan(25°) = Y/13
tan(25°)*13 mi = Y = 6.06 mi.
