A vector → A has a magnitude of 54.0 m and points in a direction 20.0° above the negative x axis. A second vector, → B , has a magnitude of 74.0 m and points in a direction 45.0° above the negative x axis. Using the component method of vector addition, find the magnitude of the vector → C = → A + → B .

Answer:[tex]|C|=125.0408406m[/tex]Step-by-step explanation:For easy calculations let's use the supplementary angles:[tex]180-20=160[/tex][tex]180-45=135[/tex][tex]A_x=54cos(160)=-50.74340152[/tex][tex]A_y=54sin(160)=18.46908774[/tex][tex]B_x=74cos(135)=-52.32590181[/tex][tex]B_y=74sin(135)=52.32590181[/tex]Now lets calculate the magnitude of the vector C: [tex]C=C_x+C_y[/tex]where:[tex]C_x=A_x+B_x=-103.0693033[/tex][tex]C_y=A_y+B_y=70.79498955[/tex]Finally:[tex]|C|=\sqrt{(C_x)^{2} +(C_y)^{2} } =125.0408406m[/tex]