Resultant Force #2 - Calculating ##\vec{F}_R##

[STEMucator]

Homework Statement

I need to calculate the resultant force $\vec{F}_R$ for the following :

http://gyazo.com/5f2d7aad6aaed178135909480016e04a

I had another thread where I clarified a few things I hope will be good now.

Homework Equations

The Attempt at a Solution

So first I should get my components. There are three vectors to consider by the looks of the diagram.

$F_N = 8N + 17Ncos(45°)$
$F_S = 10N$
$F_W = 17Nsin(45°)$

Let $F_V$ denote the final vertical force. Note that I switch the direction of south to north as to add the vectors together :

$F_V = F_N - F_S = -2N + 17Ncos(45°) = 10.02N$

$∴\vec{F}_V = 10.02N [N]$

Thus $F_R = \sqrt{(10.02N)^2 + (17Nsin(45°))^2} = 15.65N$.

To find the direction of $F_R$ consider :

$tan(θ) = \frac{10.02N}{17Nsin(45°)}$
$∴ θ = 39.81°$

$∴ \vec{F}_R = 15.65N [W 39.81° N]$

I hope all the arrows and the contexts are okay now.

 

[Redbelly98]

Looks good -- if "W 39.81° N" means 39.81° north of due west.

 

[STEMucator]

Looks good -- if "W 39.81° N" means 39.81° north of due west.

Yup, I opt to read from right to left when using that notation.

Thanks for looking over it :)