A boy Walk 1260m on a bearing of 120degree. How far south is he from his starting point
Did you draw the diagram? If so, then it should be clear that it is
1260 sin30° = 630 m
120-90 = 30 deg. south of starting point.
Well, if he's walking on a bearing of 120 degrees, he's definitely not heading south... or north for that matter. So, I guess you could say he's quite the explorer, going off in some uncharted direction where no map has gone before!
To determine how far south the boy is from his starting point, we need to find the southward component of the vector traveled on a bearing of 120 degrees.
First, let's visualize the situation. Imagine a coordinate plane with the starting point as the origin (0, 0). The bearing of 120 degrees indicates that the boy is moving in a south-southeast direction.
To find the distance south, we need to determine the magnitude of the southward component of the displacement vector.
We can break down the displacement vector into its x-component and y-component using trigonometry:
The x-component is equal to the distance traveled multiplied by the cosine of the angle:
x-component = 1260m * cos(120 degrees)
The y-component is equal to the distance traveled multiplied by the sine of the angle:
y-component = 1260m * sin(120 degrees)
Since we are interested in the southward component, the y-component gives us the answer.
Calculating the y-component:
y-component = 1260m * sin(120 degrees)
Using a scientific calculator or trigonometric tables, we find:
y-component ≈ 1091.37 meters
Therefore, the boy is approximately 1091.37 meters south from his starting point.
To find how far south the boy is from his starting point, we need to break down his movement into horizontal and vertical components using trigonometry.
First, let's consider the angle of 120 degrees. In trigonometry, angles are usually measured from the positive x-axis in a counterclockwise direction. Since we are interested in how far south the boy is, we need to determine the vertical component or the distance in the y-direction.
To do this, we can use the sine function. The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In this case, the hypotenuse is the distance walked by the boy, which is 1260 meters.
So, the equation becomes:
sin(120 degrees) = opposite / hypotenuse
sin(120 degrees) = opposite / 1260
Now, solve for the opposite:
opposite = sin(120 degrees) * 1260
Using a scientific calculator or trigonometric table, we find that sin(120 degrees) is approximately 0.866.
opposite = 0.866 * 1260
opposite = 1091.16 meters
Therefore, the boy is approximately 1091.16 meters south of his starting point.