Answer to Question #152529 in Physics for Ema Fernandez

Question

The displacement vectors A and B, when added together, give the resultant vector R, so that R = A + B. Use the data in the drawing and the fact that φ = 23° to find the magnitude R of the resultant vector and the angle θ that it makes with the +x axis.

Answer 1

$$R= \sqrt{ 6 ^ 2 +8 ^ 2 +2(6)(8)cos(90+23)° ​ } =7.9$$

$$8\cos{23°}=7.9\cosθ\\θ=\arccos0.9322=21°$$