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Vertical and Horizontal Component Calculator

Formulas

To calculate the vertical and horizontal components of a vector:

$Vc = M \cdot \sin(a)$

$Hc = M \cdot \cos(a)$

Where:

$Vc$ is the vertical component
$Hc$ is the horizontal component
$M$ is the magnitude of the vector
$a$ is the angle of the vector (in degrees)

Vertical and Horizontal Components

Vertical and horizontal components are the values of the base and height of a triangle formed with a vector as measured from the x-axis of a graph. In other words, when the horizontal and vertical components are put together to form a triangle, the resulting hypotenuse is the original vector.

Example Calculation 1

Let's assume the following values:

Magnitude ( $M$ ) = 10
Angle ( $a$ ) = 30 degrees

Using the formulas:

Step 1: Convert the angle to radians:

$a = 30 \times \frac{\pi}{180} \approx 0.524 \text{ radians}$

Step 2: Calculate the vertical component:

$Vc = 10 \times \sin(0.524) \approx 5$

Step 3: Calculate the horizontal component:

$Hc = 10 \times \cos(0.524) \approx 8.66$

Example Calculation 2

Let's assume the following values:

Magnitude ( $M$ ) = 20
Angle ( $a$ ) = 45 degrees

Using the formulas:

Step 1: Convert the angle to radians:

$a = 45 \times \frac{\pi}{180} \approx 0.785 \text{ radians}$

Step 2: Calculate the vertical component:

$Vc = 20 \times \sin(0.785) \approx 14.14$

Step 3: Calculate the horizontal component:

$Hc = 20 \times \cos(0.785) \approx 14.14$