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:

\[ Hc = 20 \times \cos(0.785) \approx 14.14 \]