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

Method 1

• Move the tail of A to the origin.
• Move the tail of B to the tip of A.
• The sum goes from the tail of A to the tip of B.

Method 2

• Reverse the roles of A and B in Method 1.

Method 3

• Move the tail of both vectors to the origin.
• Complete the parallelogram.
• The sum goes from the origin to the opposite vertex of the parallelogram.

To solve for the magnitude and direction of the sum, apply the Cosine Law and the Sine Law to the triangle formed by A, B, and A+B.