a boy walks 1260m on a bearing of120 degree, how far south is he from his starting point?
1260(sin30°)
solve it
idk sorry
99m
PLS FULL WORKING I DON'T UNDERSTAND
To find how far south the boy is from his starting point, we need to break down the 1260m in the southward direction using trigonometry.
First, let's draw a diagram to visualize the situation. We have a starting point (zero point) and a boy walking on a bearing of 120 degrees, which forms an angle with the north.
```
N
|
|
W ----|---- E
|
|
S
```
Since the boy is walking on a bearing of 120 degrees, we can say that he is facing 120 degrees clockwise from the north direction.
To find the southern component, we need to find the cosine of the angle between the north direction and the direction he is facing (120 degrees). The cosine function gives us the ratio of the adjacent side to the hypotenuse of a right-angled triangle.
In this case, the adjacent side is the southward component (distance), and the hypotenuse is the total distance the boy has walked (1260m).
By using the formula: cos(angle) = adjacent / hypotenuse, we can rearrange it to find the adjacent side:
adjacent = cos(angle) * hypotenuse
In our case, the angle is 120 degrees, and the hypotenuse is 1260m. Plugging these values into the formula, we have:
adjacent = cos(120) * 1260
Now, let's calculate it:
adjacent = -0.5 * 1260
adjacent = -630
Negative value indicates that the southern component is in the opposite direction of the chosen orientation. Therefore, the boy is 630m south from his starting point.