Equilibrium problem: Calculate the tension of each cord

[TheePhysicsStudent]

Homework Statement

Was practising an equilibrium problem (and i have done quite a few like this one before and got them right) and I am unsure Where i have went wrong here

Relevant Equations

t1v + t2v = 2.8

The question

What I did

The answer

 

[Ibix]

##\frac{\cos\theta}{\sin\theta}=?##

 

[BvU]

Not ##\tan##
(slow typist)

 

[kuruman]

Also, $$\begin{align} & T_2\frac{\cos60^{\circ}\cos40^{\circ}}{\sin40^{\circ}}+
T_2\sin60^{\circ}=T_2\left(\frac{\cos60^{\circ}\cos40^{\circ}+\sin60^{\circ}\sin40^{\circ}}{\sin40^{\circ}}\right) \nonumber \\
& =T_2\frac{\cos(60^{\circ}-40^{\circ})}{\sin40^{\circ}} =T_2\frac{\cos20^{\circ}}{\sin40^{\circ}}.\nonumber
\end{align}$$

 

[Steve4Physics]

View attachment 339689The question
View attachment 339690What I did
View attachment 339691

A couple of things worth noting...

1. If you draw the force-triangle and use the sine rule, the problem takes only a few lines of simple working. (It’s a lot quicker and less error-prone than the method you used.)

2. You have forgotten the unit in your final answer - lose one mark!

 

[Lnewqban]

 

[Steve4Physics]

To avoid any confusion, by 'force-triangle' (in Post #5) I meant this...

 

[TheePhysicsStudent]

To avoid any confusion, by 'force-triangle' (in Post #5) I meant this...
View attachment 339715

Wow thanks, I think this information may help speed time in lots of calculations i do

 

[haruspex]

Wow thanks, I think this information may help speed time in lots of calculations i do

Just in case it is not clear, when drawing a force polygon of forces in balance, the arrows join head to tail, as in @Steve4Physics' drawing.
You can also use them to find the resultant of a system of forces. In that case the resultant completes the polygon but its arrow is reversed.