vertical and horizontal components (forces)

**euclid2** · September 14th 2010, 06:27 AM

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.

**alexgeek** · September 14th 2010, 06:47 AM

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

**Soroban** · September 14th 2010, 06:51 AM

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

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