Question

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?

Answer 1

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