+x is to the right; +y is up

Vector A has a length of 3.76 cm and is at an angle of 34.5 degrees above the positive x-direction. Vector B has a length of 4.53 cm and is at an angle of 34.1 degrees above the negative x-direction.

What is the sum (resultant) of the two vectors?

The component method of vector addition is the standard way to add vectors. If C = A + B, then:
C_x = A_x + B_x
C_y = A_y + B_y

Vector	x component	y component
A	Ax = +3.76 cos(34.5) Ax = +3.10 cm	Ay = +3.76 sin(34.5) Ay = +2.13 cm
B	Bx = -4.53 cos(34.1) Bx = -3.75 cm	By = +4.53 sin(34.1) By = +2.54 cm
C	Cx = Ax + Bx Cx = -0.65 cm	Cy = Ay + By Cy = +4.67 cm

State the resultant like this:

C = -0.65 cm + 4.67 cm

Or, glue the two components of C together to find the magnitude and direction of C.

C² = C_x² + C_y² = 0.65² + 4.67²
C = 4.72 cm

tan(q) = 4.67 / 0.65

q = 82.1 degrees

So, the resultant vector has a magnitude of 4.72 cm and is 82.1 degrees above the -x direction.