A resultant vector has a magnitude of 25m?s with an angle of 20 degrees counterclockwise of east. draw the resultant on a coordinate plane, Find the x-component. Find the y-component

as with any vector of length r on an angle of t,

x = r cos(t)
y = r sin(t)

So, plug in your numbers.

To draw the resultant vector on a coordinate plane, we need to use the given magnitude and angle.

1. Draw a line segment with a length of 25 units. This represents the magnitude of the resultant vector.
2. Start from the origin (0,0) and draw the line segment in the direction of 20 degrees counterclockwise of east.

Now, to find the x and y components of the resultant vector:

1. The x-component represents the horizontal displacement of the vector. To find it, we can use the cosine function: cos(θ) = adjacent/hypotenuse.
In this case, θ is the angle counterclockwise of east (20 degrees) and the hypotenuse is the magnitude of the vector (25 units).

x-component = adjacent = magnitude * cos(θ)
x-component = 25 * cos(20°)
x-component ≈ 23.83

2. The y-component represents the vertical displacement of the vector. To find it, we can use the sine function: sin(θ) = opposite/hypotenuse.
In this case, θ is the angle counterclockwise of east (20 degrees) and the hypotenuse is the magnitude of the vector (25 units).

y-component = opposite = magnitude * sin(θ)
y-component = 25 * sin(20°)
y-component ≈ 8.58

Therefore, the x-component is approximately 23.83 and the y-component is approximately 8.58.