Trig/Physics
posted by Nycw .
Joe walks 5 miles in the direction degrees North of East, and then 10 miles in the direction 20 degrees West of North.
(a) How far is Joe from his starting position?
(b) In what direction is Joe from his starting position?

You left out an important number that is needed to compute the answer. It should follow the first word "direction". How many degrees is the first direction North of East?

Hi, sorry it was 30 degrees North of East.

total displacement north
= 5 sin 30 + 10 cos20
= 2.5 + 9.397
= 11.897 miles
total displacement east
= 5 cos30  10 sin20
= 4.33  3.42
= 0.91 miles
(a) sqrt[(11.897)^2 + (0.91)^2]
= 11.93 miles
(b) direction = tan^1 0.91/11.897
E of N
= 4.37 deg E of N 
Hi, thank you so much. Everything I tried hit all around the borders, but just was not working out correctly. I really appreciate your help.