Question

You went 100 miles north and 14

miles east. What is the angle of
displacement (round to the nearest
whole number)

Answer 1

82 degrees

Step-by-step explanation:

consider your staying point to be the center of a circle. this center has the coordinates (0, 0).

the radius of the circle is the distance you walked East (14 miles).

I assume your teacher means as "angle of displacement" the angle between the East-West line going through your starting point and the direct line from your starting point to your current position.

then the 100 miles North is tan(displacement angle)×14.

as it is the same, if you first went North and then East, or the other way around. you end up at the same point, with the same coordinates.

so, again.

100 = 14×tan(angle)

tan(angle) = 100/14 = 50/7 = 7.142857...

the displacement angle is then 82 degrees.