How to solve the magnitude of a vector when it is unknown?

Question

can someone help me to solve or find the magnitude of a vector when it is unknown?

Problem:

Vector A has magnitude of 188 units pointing 30.0 degrees North of West.Vector B points 50.0 degrees East of North, and Vector C points 20.0 degrees West of South. These three vectors add to give a resultant vector that is zero. Find the magnitudes of Vector B & C.

Answer 1

The easiest way to solve this is through a graphical solution. But to do this you're gonna need a good ruler and some sort of angle measurer. First draw vector A, in a certain scale, let's say 1 in = 10 units. That means you'll be drawing a straight vertical line which has a length of 18.8 in.

Next you draw vector B from the edge of vector A 50 deg east to north.

Draw a very very long line.

Next you draw vector C from the other edge of vector A, 20 deg west to south. Again draw a very very long line.

You'll then get a intersection where the line representing vector B & C meet. Measure the line, from that intersection to the edge of vector A. Multiply the measurement with the scale you've already stated in the first step (1 in = 10 units).

Et voila!! You got the magnitude of each vector