A boy walks 1260m on a bearing of 120 degree. How far south is he from his starting point
since his heading (NOT bearing!) is E30°S, he winds up at
1260sin30° = 630 m south of the starting point.
This answer is incorrect. The given bearing of 120 degrees is not the same as the heading of E30°S.
To solve the problem, we need to find the horizontal and vertical components of the boy's displacement.
The horizontal component can be found by multiplying the distance traveled by the cosine of the bearing:
1260 cos(120) = -630
Note that we get a negative value because the bearing is measured clockwise from North, while the x-axis is usually measured counterclockwise from East.
The vertical component can be found by multiplying the distance traveled by the sine of the bearing:
1260 sin(120) = 1089.25
Note that we get a positive value because the y-axis is usually measured upward.
So the boy is 630 meters west (left) and 1089.25 meters south (down) from his starting point.