# Thread: vertical and horizontal components (forces)

1. ## vertical and horizontal components (forces)

find the horizontal and vertical components of a force of 75N that acts in a direction forming an angle of 51 degrees with the vertical.

2. Just use trig,
$F_v = 75 \cos(51)$
$F_h = 75 \sin(51)$

3. Hello, euclid2!

Did you make a sketch?

Find the horizontal and vertical components of a force of 75N
that acts in a direction forming an angle of 51 degrees with the vertical.

In the diagram, "d" represents "degrees".

Code:
      |           o A
|         * :
|    75 *   :
|     *     :
|51d        :
| * 39d     :
O * - - - - - + - -
|           B

In right triangle $ABO\!:\;\;O\!A = 75,\;\angle AOB = 39^o$

The horizontal component is $OB.$
The vertical component is $AB.$

Therefore: . $\begin{Bmatrix} \cos39^o \:=\:\dfrac{OB}{75} & \Rightarrow & OB \;=\;75\cos39^o \;\approx\;58.3 \\ \\[-3mm]
\sin39^o \:=\:\dfrac{AB}{75} & \Rightarrow & AB \:=\:75\sin39^o \;\approx\;47.2 \end{Bmatrix}$