physics!
posted by hana .
A truck driver travels a distance of 100 miles due East. He then turns at an angle of 35 degrees S of E and travels a distance of 50 miles.
What is the resultant displacement?
What is the direction?

Just add the two vectors.
The eastward displacement is
X = 100 + 50 cos35 = 140.96 miles
The northern displacement (assuming north is positive) is
Y = 50 sin35 = 28.68 miles
(The minus sign is there because the second vector is south of east, not north).
Total displacementis
= sqrt[(140.96)^2 + (28.68)^2]
The direction(measured south of east) is tan^1 (28.68/140.96) = 11.5 degrees