Question being asked: Use the trigonometric ratios and Pythagorean theorem to add the vectors given in the figure. Determine the magnitude and direction of the resultant.

Question

The problem has two vectors, the first labeled A is pointing towards the origin in quadrant 1. With A=90.3 and the angle equaling 10.3 degrees.
The second b is pointing away from the origin with B=53.1 and the angle equaling 17.3 degrees.

So I know you move A so that the tail is at the origin. However after that I am not sure how to resolve the vectors into x and y components and all that comes after. Any help would be appreciated.

Answer 1

Yo are correct that you place both tails at the origin. Then for each vector v (that is, either A or B),
x = v cosθ
y = v sinθ
Remember your polar coordinates?
Then just add the x and y values to get the resultant.

Or, you can consider them as complex numbers, and that will take care of the x and y values for you
90.3 cis190.3° + 53.1 cis17.3° = 38.15 cis -3.13°

Or, geometrically, draw a parallelogram with sides A and B, and the diagonal will be the resultant.

Answer 2

Or, you can put the point of A at (0,0) and the tail of B at (0,0) and then A+B is just the vector from the tail of A to the tip of B.

review vector addition, or search online for many more examples.