A boat sails 5.0(45 degrees W of N). It then hanges direction and sails 7.0km(45 degrees S of E) where does the boat end up with reference to its starting point.?

Question

A boat sails 5.0(45 degrees W of N). It then hanges direction and sails 7.0km(45 degrees S of E) where does the boat end up with reference to its starting point.?
Please explain steps
answer is 2km(45 degrees S of E)

Henry · Accepted Answer

A = 5.0km[135o]
B = 7.0km[315o]

D = A+B
D=(5.0*cos135+7.0*cos315)+i(5.0*sin135+
7.0*sin315
D = (-3.54+4.95) + i(3.54-4.95)
D = 1.41 - i1.41 = 2km[-45o]=2km[45o S of E].

NOTE: The cosine function was used to
find the hor. components; the sine function was used to find the ver. component.