Arny flies due east from san francisco to washington, d. c., a displacement of 5600. km. he then flies from washington to boston, a displacement of 900. km at an angle of 55. degrees east of north. what is arny's total displacement?

The total displacement is the distance AC (San francisco to Boston)

we apply the law of cosines on triangle
b²=a²+c²- 2 .a .c. cos B

(look at the image)

cos B= cos(180-55)=cos(125)= -0.57
b= sqrt((5600² + 900² +2.5600.900.0.57))=6157.56Km