A sailboat travels 13 miles at 27 degrees east of north. Then travels 18 miles at 35 degrees south of east. What is the result of the entire trip? (Distance and direction)

Question

It would be also be great if you told me how you worked it out. Thanks!

Answer 1

Step 1: make a diagram
on mine, the trip forms a triangle with sides of 13 and 18 miles and an angle of 82°
between them

a clear case of the cosine law: let the distance be d
d^2 = 13^2 + 18^2 - 2(13)(18)cos82°

continue, let me know what you get

Answer 2

Wouldn't the angle be 62° rather than 82°?
Because 27+35=62?

Answer 3

All angles are measured CW from +y-axis.
D = 13mi[27o] + 18mi[125o]
D = (13*sin27+18*sin125) + (13*cos27+18*cos125)I
D = 20.6 + 1.26i = 20.64mi[86.5o] CW.