Find the magnitude and the direction (to the nearest degree) of the resultant of each of the following systems of forces

Question

a. forces of 3 N and 8 N acting at an angle of 60° to each other

Answer 1

Complete the parallogram and draw in the resultant, which would be the diagonal.
R^2 = 3^2 + 8^2 - 2(3)(8)cos 120° = 97
|R| = √97 = appr 9.85 N

or , place one vector along the x-axis, ....
|R| = 3(cos0, sin0) + 8(cos60,sin60)
= <3,0> + <4,6.928..>
= <7,6.928>
= √(49 + 48)
= √97