A vector points 34.8 degrees to the Northeast with magnitude 15. What are the north and east components that make up the remainder of the triangle?
a(x) =a•cos34.8º=…
a(y) = a•sin34.8º=…
34.32
To find the north and east components of the vector, we need to break it down into its vertical (north) and horizontal (east) components.
Given that the vector points 34.8 degrees to the Northeast, it means that it is 34.8 degrees counterclockwise from the positive x-axis (east) and 45 degrees counterclockwise from the positive y-axis (north).
To find the north component, we can use trigonometry. The angle between the vector and the y-axis is 45 degrees, and the magnitude of the vector is 15. Therefore, the north component can be found using the formula:
North component = magnitude × sin(angle)
North component = 15 × sin(45°) = 15 × √(2)/2 ≈ 10.61
So, the north component of the vector is approximately 10.61.
To find the east component, we can also use trigonometry. The angle between the vector and the x-axis is 34.8 degrees, and the magnitude of the vector is 15. Therefore, the east component can be found using the formula:
East component = magnitude × cos(angle)
East component = 15 × cos(34.8°) ≈ 12.32
So, the east component of the vector is approximately 12.32.
Therefore, the north component is approximately 10.61 and the east component is approximately 12.32.
To determine the north and east components of a vector, we can use trigonometry.
First, let's consider a right triangle with an angle of 34.8 degrees. The hypotenuse of this triangle represents the magnitude of the vector, which is 15 units. We want to find the lengths of the legs of the triangle, which correspond to the north and east components.
In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. So, we can use the sine function to find the north component:
sin(angle) = opposite / hypotenuse
sin(34.8 degrees) = north component / 15 units
north component = sin(34.8 degrees) * 15 units
Using a calculator, we find that sin(34.8 degrees) ≈ 0.577.
north component ≈ 0.577 * 15 units
north component ≈ 8.66 units
The north component of the vector is approximately 8.66 units.
Similarly, we can use the cosine function to find the east component:
cos(angle) = adjacent / hypotenuse
cos(34.8 degrees) = east component / 15 units
east component = cos(34.8 degrees) * 15 units
Using a calculator, we find that cos(34.8 degrees) ≈ 0.816.
east component ≈ 0.816 * 15 units
east component ≈ 12.24 units
The east component of the vector is approximately 12.24 units.
Therefore, the north and east components that make up the remainder of the triangle are approximately 8.66 units and 12.24 units, respectively.