an automobile travels 3 miles due north then 5 miles north of east. what is your resultant displacement?

Answer 1

North of east is not a direction

Do you mean Northeast? North by East? North North East ?

I will assume Northeast which is 45 degrees north of east

If so then:
North 3 + 5 sin 45 = 6.54
East= 0 + 5 cos 45 = 3.54

distance = sqrt (6.54^2 + 3.54^2)
= 7.43 miles
tan angle north of east = 6.54/3.54
angle north of east = 61.6 degrees
so bearing from origin clockwise from north = 90 - 61.6 = 28.4

Answer 2

Please correctly understanding.