A person walks from point A to point B as shown in the figure below. What is the person's displacement relative to A?

Question

What is the magnitude?
What is the direction ° (counterclockwise from the +x-axis)?

Answer 1

OK, I found the figure at
http://www.webassign.net/wb/3-30.gif

All you have to do is use a little trig and add up the vertical and horizontal displacements.

Four vectors are being added. In the +y direction, the change in position is
Y = 20 sin 30 + 30 - 20 sin 45
= 25.86 m

You do the +x displacement, which is
X = 20 cos30 -40 + 20 cos 45, which is a negative number.

Use the Pythagorean theorem for the magnitude of the displacement.

The direction angle is in the second quadrant and the tangent of the angle from the +X axis is Y/X

Answer 2

27m at 72 degrees