Question

A hiker starts at his camp and moves the following distances while exploring his surroundings: 255 m east, 125 m at an angle 30.0° north of east, and 178 m at an angle 12.0° south of east. Find his resultant displacement from camp.

Answer 1

Find the eastward and southward components of displacement:

$A_N=0,\\ A_E=255.\\ B_N=125\sin30°,\\ B_E=125\cos30°,\\ C_N=-178\sin12°,\\ C_E=178\cos12°.\\\space\\ R_N=A_N+B_N+C_N=25.5,\\ R_E=A_E+B_E+C_E=537,\\\space\\ R=\sqrt{R_N^2+R_E^2}=538\text{ m},\\\space\\ \theta=\arctan\frac{R_N}{R_E}=2.7°.$