A boy walks1260m on a bearing of 120. How far south is he from his starting point.
630m
answer
To find how far south the boy is from his starting point, we need to consider the bearing angle of 120.
A bearing angle is typically measured clockwise from the north direction, meaning that a bearing angle of 120 degrees is in the southeast direction.
To calculate the distance south, we can use trigonometry. In a right-angled triangle, the sine function (sin) relates the length of the side opposite an angle to the length of the hypotenuse. Since we are interested in the side opposite the angle of 120 degrees, and we know the length of the hypotenuse (1260m), we can use the sine function.
sin(120) = opposite / hypotenuse
sin(120) = opposite / 1260
To solve for the opposite side (the distance south), we rearrange the equation:
opposite = sin(120) * 1260
opposite = 0.866 * 1260
opposite ≈ 1091.76
Therefore, the boy is approximately 1091.76 meters south from his starting point.